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.

RAW

From strict reading of the ASI, you shouldn't be able to, since it does not say "You can't increase an ability score above your current cap" or something on these lines, it just says "You can't increase [...] above 20".

Rules as (probably) Intended

Now, is it intended? Probably not.

In the PHB, the only way to go over your cap is through Barbarian's Primal Champion feature, which is at 20th level and you are not getting any more ASIs after that.

So one possible reading on this is that it's worded as it is for simplicity, since they were not considering the items on DMG.

The problem is that, from my experience, the DMG is written (more) vaguely (than the PHB), which might even be intentional since it's supposed to be read by the DM and he can decide whatever he wants. This means it's probably implied that increasing the maximum score by 2 (to 22) allows you to increase your stat score to 22 by any mean, including ASI.

A further indication that you should be able to do it is that every mean of increasing your stats says something on the lines of "up to 20" (AFAIK), instead of "up to your cap". This means any feature increasing your cap doesn't do anything, since everything is hard capped in its own text anyway (Ioun Stone as another example besides ASI).

For clarity, what I mean here is that there would be no reason to word it as "your maximum for that score increases by 2" instead of "up to any value" or "not hard capped at any value" or anything like this if it was not supposed to influence any other item or feature.

About your last question

In fact, is 20 even the maximum for your ability score when using items; the quote seems to only apply to Class Features.

The quote is a general rule. This shouldn't matter though, because as far as I know, the items explicitly state their cap (Deck of Many Things' star card caps at 24, Ioun Stones cap at 20, etc).