I'm glad you like it! And let me know how it works out, if you wind up play-testing it. The Charisma thing should be totally fine -- I only switched it to Intelligence for flavor reasons, not balance reasons. (In fiction, the psychic is far more likely to be the brainy one than the likable one. I could see a strong argument for Wisdom as the casting stat, but the game doesn't need any more Wisdom casters right now.)
I've been following along with this effort and I like where you're going with it. I'd probably do something similar if I made a full class.
3.0 tried this for Psionics, and it was painful. You either had a very restricted power selection or super bad MAD.
I think you could make it work by subclass. E.g. if you're primarily into Telepathy, you use Charisma, most of your powers are telepathic in nature, you can pick up some number of other stuff (shapeshifting, telekinesis, what have you) and still use Charisma with them. But you'd get more telepathy powers, and your special abilities would only work in conjunction with telepathy abilities.
The other thing I could see working, is each category uses the best of two abilities.
Mind = Cha or Int
Spirit = Cha or Wis
Life = Wis or Con
Matter = Con or Int
This would allow limited mix+match without getting MAD. Basically if you pick "adjacent" categories you can use the ability they share; if you pick two "opposite" categories you have a MAD of 2 abilities; but picking any 3-4 categories you can still do with a MAD of only 2.
Sorcerer is an extremely broad concept that needs to cover a lot of characters. This is one of the reasons it's so hard to design a good sorcerer class. I think "psychic" or "psion" can be portrayed much more limited way, so that it sorta fits inside the sorcerer, which is what I tried to do here, but I'm not sure the reverse is true. I don't think most people would consider Elsa or Rand al-Thor to be psychics. And treating Jean Grey and Eleven as sorcerers is kind of weak, too; it only sorta works. In fact, the only reason to do it this way is in the interest of rules-minimalism: if somebody really wanted to play a psychic, this subclass is just an excuse for reskinning the sorcerer.
If I were to do Psion as a full class, I would go in a very different direction: I'd make it as weird and sci-fi as possible. When I look at the older D&D use of psionics, especially 2E, I get a very bizarre, weird-fantasy feel, and that's cool. It's why it works in Dark Sun and why newer iterations try to tie it into the Great Old Ones or the Far Realm. (I personally don't like the Far Realm as I think it kind of waters down the existential horror to stick it all in a specific place.) This would bring a lot more to the game, for me.
I guess I'd rather introduce new fluff to the game (psychic weirdness) using existing mechanics, than rehash old concepts (sorcerer) with new mechanics.
Although... now that you've got me thinking about it... I may take a stab at a full class just to see if it can be done...
