Still reading through the book, so just throwing out some general ideas
Personally don't like the idea of Wisdom replacing Dexterity for Initiative checks, doesn't make sense to me. It seems good to me. Wisdom is the awareness, which allows to start reacting quicker(Acting in a Surprise Round), while Dexterity is how fast you react once you are aware(the Initiative).
I like the idea of Charisma replacing Wisdom for Will saves, as I attribute Charisma to 'force of personality,' so you're counteracting someone's attempt to influence it, with the force of it. Wisdom is more general awareness.
The main problem with Charisma is that it's not a stat stat. It's more of a qualitative than quantitative attribute, and it relates directly to how we play our character. We don't roll Charisma skill checks between PCs because that would be one sided to the guy who decided Cha wasn't a dump stat. We roleplay out our interactions. Someone mentioned earlier that it is up to the GM to increase Cha importance through the situations they're put in, and I agree. Cha should mainly affect PC-NPC interactions. I really like the idea of group social checks so that somebody doesn't do something wrong. But, GMs could apply Cha to change the story, an immeasurable, yet interesting effect, as well as character backstories. I'm going to pick on the soldier a bit because it seems like the classic Cha dump. You want your soldier to be a badass on the field, but he could be socially inept and not even know it. In a military setting, it could keep him from getting promoted, because nobody likes him. Yeah, he's strong on the field, but people consider him more of a meat shield than a comrade. They don't want to hang out with them outside of work, could think he's a blowhard/gloryhound, etc, etc. Let the player play how he wants to play the character, but the Cha could really affect how NPCs can perceive them.
On a more stat basis, I'd rework the Intimidate rules somehow so that Charisma plays a more significant role in defending against an Intimidation check. That Shaken condition that can be applied to a PC can really mess them up. In addition, perhaps add a Leadership skill, or a feat tree that could add certain benefits in combat/social situations. For example, removing Shaken, reducing terrified, coordinating attacks for improved tactical options. I think it would be really cool to have some sort of leadership/telepathy combo to help someone else with a will save. Don't know if this would step on Envoy's toes though, sooooo, maybe.
Solarian seems to be having some problems from what I'm reading here.... Well, an option that pops out to me is, why not simply add to the Solarian weapon feature that they may use Charisma instead of Strength when adding damage? Would allow the Solarian to focus more in the Cha stat, reduce the ability spread, and provide a competitive edge to lower levels that phases out at higher levels when someone said Solarian damage gets better. Similarly, with the armor, use Charisma instead of Dex for AC.