This sounds very much like a bug. The Black Book in question is merely one of many, and all but one of them grant three choices, of which you pick one. Also, your main level should never, ever go up except via leveling skills, so if your skills weren't increased at the same time, it's 100% a bug. And unless you're made a skill Legendary (see below), 81 is the normal cap, so your skills would need to be basically all 100. Even if they've increased, though, it's basically guaranteed to be a bug.
As to your side note, yes, there is a way to get more perk points. Skyrim patch 1.9 added the ability to make a skill that has reached 100 Legendary. This resets the skill to its base level of 15, while also giving back the perk points that skill had (since many of those perks are ones you're no longer qualified for). Because the skill was reset, you can level it up to 100 again, gaining character levels as you go.
Additionally, if you're not willing to give up your skill levels for more perks, you can simply complete the main Dragonborn questline. The rewards at the end include an ability to reset the perks on a tree at a cost of one Dragon Soul. Your level in that skill remains as it was, but all the perks are refunded. It's not quite the same as gaining new perks, but it can be very useful for things like fixing mistakes, and also refunding perk points on crafting skills. You might not want to reset your Enchanting, in case you need it again, but you can reassign the perk points for a while. If you need your Enchanting perks again, a quick trip to Solstheim and a couple dragon souls is all it takes.
Completing this quest in favor of the Nords will provide you with the availability of four more favor quests, each offering a leveled amount of gold as reward. After completion of Retaking Thirsk, Kuvar will offer Heavy Armor training and Blacksmith services.
Completion in favor of the Rieklings gives no monetary or item rewards. After completion you will be able to have a Riekling as a pet. They take up a pet slot, but you can access their inventory and have a normal follower.
In addition, the game has a chance to randomly spawn up to three Rieklings to assist you while in combat. Reportedly anywhere in Skyrim or Solstheim.
Best Answer
No, there is simply no way to finish the quest without killing Miraak. Furthermore, there is no way to kill Hermaeus Mora (in the base game/DLC, at least).
However, I found this oddly specific mod that apparently allows you to do exactly what you've described in the question. The mod allows you to cast Bend Will on Miraak and team up with him against Hermaeus Mora, as well as unlocks Miraak as a follower and marriage candidate.
Unfortunately, nothing on the page indicates whether or not this mod is compatible with Skyrim Special Edition. This appears to be a port of the original mod that works in the Special Edition, but it looks like it was combined with other mods.