RAW allow it, but there are some setbacks.
Crawford also agrees (thanks to V2Blast for that).
Grier: If you find multiple books or are long lived, can you get this bonus multiple times?
Crawford: Yes.
While you have done an excellent work in tracing the requires rules and components to make all of this work, there are somethings you need to rethink.
3200 years is an immensely long time.
Consider that, every time the Wizard freezes himself in time in his dimension, the entire world ages a century. Civilizations rise and fall, continents change, plagues ravish, dragons destroy. Industrial revolutions rise, ice caps melt, Gods wage war upon each other. While your Wizard could ignore all of these, someone that didn't take a long time every century to follow up on all of these events would soon find themselves completely lost in the world, not knowing where to turn to anymore, and only imagining how the carriages without horses worked.
Learning all the books takes a long time every time, where food, water, safety, and above all sleep, are necessary.
The Wizard cannot just spend 300h studying books. By the 5th day, he'd die of exhaustion (seriously, by RAW, 5 levels of Exhaustion kills you!). He needs to rest everyday, to take care of his health, and would take a lot more time than the minimum you've allotted.
After a few centuries, the Wizard can barely describe a place to appear at.
Imagine he had a home to come back to. After a century, it's probably been taken over by some other resident. After another, maybe it's been abandoned. Another and it is now the home for devils and mindflayers. The nearest town has grown to a big empire. In another century, it has waged war and dwindled in size. In another, a plague has consumed anyone who was left there. As the world changes, the places the Wizard has to come back to all vanish. He can always come back with some general description, but he has no real place to come back, no place he can recognize. He stops knowing how the world behaves, he doesn't know what is dangerous anymore, and how to fight the new threats.
Does a sane man really want to throw everything away to become powerful?
Every story has a big villain. Some demon risen from Hell (Tarrasque), some alien from another planet (Megatron), some angel fallen from grace (Sauron). Your Wizard would become this villain. He attained immense power over the centuries but lost touch with the world. All he has is power and the strength to use it, but he isn't part of this world anymore. The new races who have emerged will barely recognize him. He cannot bond with anyone, as everyone is so dumb and boring compared to himself. He is, in all respects, a higher being. What does he want to do now? Control the world, for the greater good? Or destroy it?
How would the world see him?
A creature emerges out of thin air. Taller, stronger, grander than anything these primeval races have ever witnessed. The air around him fizzles with raw arcane powers. He speaks a forgotten language, no one comprehends it anymore. The crowd gathers in awe. A flash of flames appears, an exhibition of his skills, but most of the crowd looks scared, and starts moving away. This alien god looks angry at the lack of adoration by these puny creatures. In a swift gesture, all of them are incinerated. They will bow down to their new leader or perish. Accept this wicked salvation or be destroyed.
This is how villains are born.
Clarification: Only use one hand crossbow because a second actually interferes with itself and allows fewer attacks.
Level 10 Hunter Ranger (or Hunter 8 / Fighter 2)
Start off with a Human; Variant with the Crossbow Expert Feat.
Starting stats: Str 10 - Dex 16 (Human +1) - Con 14 - Int 8 - Wis 14 (Human +1) - Cha 12
Strength, Intelligence, and Charisma are interchangeable. Dexterity is your main stat, so you want that as high as possible. Constitution is useful for staying alive and Wisdom is your casting stat.
Level 1 - Ranger
Depending on how you get your gear, you going to want to get Studded Leather as soon as you can, and a Hand Crossbow (HXB, from now on). It wouldn't hurt to have a Rapier and a Heavy Crossbow on hand, as well.
Attack Counter: 2 HXBor 1 Melee 1 HXB
Level 2 and 3 - Ranger (Hunter)
Hunter path taken and Hordebreaker unlocked. Take the Archery Fighting Style for +2 to hit. This is where the fun starts. You get a free other attack against an adjacent enemy to one of the enemies you attack this round!
Attack Counter: 2 HXB + 1 adjacent or 1HXB + 1 Melee + 1 adjacent Melee
Level 4 - Ranger (Hunter)
Ability Score increase to Dexterity. You're just making yourself better at everything. +1 Damage, +1 Attack, +1 AC.
Attack Counter: 2 HXB + 1 adjacent or 1HXB + 1 Melee + 1 adjacent Melee
Level 5 - Ranger (Hunter)
Extra Attack! And Level 2 Spells, which means Hail of Thorns.
Attack Counter: 3 HXB + 1 adjacent or 1HXB + 2 Melee + 1 adjacent Melee or Hail of Thorns to AoE 1 of your attacks + 3 attack chances
Level 6 - Ranger (Hunter)
Honestly, if you're going to multiclass, you could do it here instead of later (I talk about it in levels 9-10), but you'd delay your Ability Score Increase; level 6 is a snooze level, so I wouldn't blame you.
Attack Counter: 3 HXB + 1 adjacent or 1HXB + 2 Melee + 1 adjacent Melee or Hail of Thorns to AoE 1 of your attacks + 3 attack chances
Level 7 and 8 - Ranger (Hunter)... Feat? or ASI?
Sharpshooter has some good bonuses for attacking through cover (including attacking behind other creatures) and at long range, but the big-ticket item here is the damage boost. +10 vs scrubs is huge - on top of your 1d6+4 (average 7).
Maxing out your Dex is a great help. +1 to most of the things you're doing in combat (to hit, damage, and AC) makes for a good day.
The choice is yours between pure "kill it" and being ever so slightly more well rounded.
Choices aside, you get one more 2nd-level Spell Slot, which means one more Hail of Thorns.
Attack Counter: 3 HXB + 1 adjacent or 1HXB + 2 Melee + 1 adjacent Melee or Hail of Thorns to AoE 1 of your attacks + 3 attack chances
Level 9 and 10 - A choice.... stay Ranger (Hunter) or dip Fighter or dip Rogue
Staying in Ranger (Hunter) gives you access to 3rd level spells at level 9 (i.e. - Conjure Barrage twice per long rest) and gives some features I don't care about (Looking at you, Hide in Plain Site)
Taking 1 level in Rogue gives you a few things and let's you still get access to 3rd level spells; mainly, you get Expertise and 1d6 Sneak Attack once a turn. Not a huge boost, but it's something.
I'm a sucker for a 2 level dip into Fighter; I love action surge. This would net you another Fighting Style (Protection, probably), Second Wind for a tiny bit of survivability, and Action Surge for another... uh... Action. This would only give you two more attacks once per rest (or whatever you use it for), but it's something.
Attack Counter: 3 HXB + 1 adjacent or 1HXB + 2 Melee + 1 adjacent Melee or Hail of Thorns to AoE 1 of your attacks + 3 attack chances or Conjure Volley.
Additional Notes
When fighting a single large enemy, it may be worth it to use Hunters Mark to stack on an extra 1d6 with every hit. However, with multiple smaller enemies, you're likely to have to keep swapping your Mark, which you could just use your bonus action to attack with.
level 11, Rangers (Hunter) gain the Multiattack - Volley class feature, which sounds like exactly the goal of this class:
Volley
You can use your action to make a ranged attack against any number of creatures within 10 feet of a point you can see within your weapon's range. You must have ammunition for each target, as normal, and you make a separate attack roll for each target.
Honorable Mentions
Bard
Level 6 Lore Bard gets access to Hail of Thorns via Magical Secrets, and six times! Take 3 levels in Hunter for the Horde Breaker feature or 2 levels in Fighter for Action Surge.
Or Level 10 Valor Bard also gets access to an extra attack, Magical Secrets (Hail of Thorns! or Conjure Volley. Why not both?)
The only problem is how long it takes for these builds to "come online".
Fighter
Fighters get the most attacks, so this seems like an ideal choice. But with the level 10 restriction, we don't get much bonus over other martial classes.
Eldritch Knight is appealing for the handful of spell options; you could combine it with Hunter 3 for Hordebreaker for some fun combinations with Warmagic (Green Flame Blade works with ranged weapons within 5 ft.... because of reasons). The main reason this is rejected is because it doesn't feel on theme with what you want.
I wanted Battlemaster to work, but most of the Martial moves implement Melee Attacks.
War Cleric 2 / Hunter 8
Ranger and Cleric use the same Ability Score and you can upgrade to a Heavy Crossbow instead of a Hand Crossbow 5 times per long rest. One use of Guided Strike per rest to give you a +10 that attack that really has to hit. A couple extra healing slots never hurt anyone.
Again, I like this build, but it doesn't seem on theme with what you want.
Rejects
Warlock + Anything
I wanted this to work pretty badly (See here for an amazing breakdown of what a Warlock and a Hand Crossbow can accomplish). And I think that Pact of the Blade Hexblade Warlock 12 / Hunter 3 is pretty scary. 2 Attacks with +10 damage from Life Drinker and the bonus attack from Crossbow Expert AND the Hordebreaker from Hunter 3... alas, level 15 is not level 10 and there's not much value in Warlock 7 / Hunter 3.
That, and it requires a magical Hand Crossbow... Which can theoretically be loopholed with a multiclassed sorcerer willing to extend Magic Weapon, but I digress.
Barbarian
Doesn't play nice with dex-based ranged weapons.
Paladin
Paladin is a tank, or a nuker. Not a lot of synergy with spreading your damage around.
Rogue
Rogues do not get enough attacks to make this class super useful on its own.
Arcane Archer
Requires Shortbows or Longbows.
Best Answer
We can do 360’ with a few magic items and guardian of nature.
Attunement free magic items: +60'
Goggles of night (does not require attunement):
Magic items requiring attunement: +180'.
Verminshroud (EGtW, pg. 273):
Robe of Eyes (does not stack with guardian of nature):
Wreath of the Prism (EGtW, pg. 274):
Color Dragon Mask (RoT):
Silken Spite (EGtW, pg. 277):
Orb of the Veil (EGtW, pg. 268):
Axe of the Dwarvish Lords (dwarves only):
All of these items are equivalent to an additional 60’ on top of your racial 60’, so pick goggles of night and 3 requiring attunement for a darkvision out to 300’,
Spells: 120'
We can cast the 4th level spell guardian of nature:
This gives +60' on top of our racial 60'
All together now: 120' (guardian of nature) + 60' (goggles of night) + 3 x 60' (3 magic items of your choice) = 360'
Honorable Mentions: The dimensional loop from Acquisitions Incorporated extends dark vision by 30'. The spell true seeing allows the caster to see up to 120' in darkness, but doesn't properly grant dark vision, so it does not interact with the items listed for the optimization part of this answer.