Is there anything I can do for being disqualified after a psych consult for not showing remorse for charges that were dismissed?

Nope. MEPS is deigned to keep you out, not let you in.

My friend got disqualified for the same reason. Even though he didn't do it they still wouldn't let him in. So our recruiter asked him to write a letter and he said "how can I have remorse for something I didn't do". Moral of the story he couldn't enlist.

Is this a MEPS thing? If it is then no, you have no recourse for being denied an opportunity to enlist unless it violates your civil rights. This does not qualify.