Heroes 5.5 WarGame Edition - Tactical Edition.

Is it possible to change an arch-enemy without a forced connection to a Castle?

No, it isn't. But this connection can be ensured through scripts; the question is how it will look.

The upcoming mod completely eliminates late-game mana issues.

Why would it? At the beginning of the day, you'll have at least 40% mana due to basic mana regeneration (with 60% Mysticism, and around 30% Intelligence). Dark Ritual allows you to replenish the remaining 40-70% at the cost of logistics, and only at the beginning of the day. This is a good option to enhance spellcasting, just like Mysticism. In the final stage, due to the limit of 5 mana per unit of knowledge, there still won't be an excess of mana.

But tying the ultimate ability to an artifact, in my opinion, is not a good idea.

I don't see any downsides to this. Upgrading with the ultimate ability becomes more varied, but still remains rare. The artifact becomes desirable, rather than just useless (+1 to a skill), taking up a relic slot. Finally, the logic is preserved: 4 perks - 4 skill levels. I actually believe that the ability to upgrade the ultimate ability without a pendant was a bug.

I still see the 2-(1)-2-(2)-4 perk system as ideal.
Numbers in parentheses indicate connections.
If we choose one line, initially only 1 primary skill of that school will be offered instead of two, which immediately increases the probability. Considering that 4 perks of level 3 are stronger than the previous ones.

I carefully considered your option and came to the conclusion that it is interesting, but the classic option with 3 perks at the start is more logical and stronger. Simply because it provides more skill upgrade options and is not actually more random than the random selection of new skills.

Your 2+2+4 option, although it simplifies the upgrade process a bit, provides only 6 skill upgrade options (I mean a complete upgrade, 3 perks).
This is very few; even with 5 perks (instead of 8), 5-6 options are provided. And with full skills (7-9), the variability is twice as high. Note that the more perks that lie at lower levels, the more options there are. That's why I have so few level 3 perks.

Also, a key feature of the scheme is the fact that only really cool perks are left or enhanced, there are no narrowly situational or mediocre perks, as in TE (where they left the trash in order to make it more difficult to obtain "imba" perks).