My initial impression of the OP was that there's absolutely nothing I would change. The third season wasn't the best, but it was still Star Trek, and there's not a lot you could change without turning the show into something else completely. Most of the other posts here just underscore that. (Trek without Kirk or McCoy? Unthinkable. Serialized storytelling? Wasn't a thing in the '60s.)For the third season, I suppose the big thing I'd do is back a big dump truck full of money out in front of Gene Coon's house to get him to come back to the show. And I'd bring Robert Justman in as the producer instead of Fred Freiberger.
I'd try to keep "Spock's Brain" and "The Enterprise Incident" closer to Gene Coon's and D.C. Fontana's original concepts...
I think it'd be interesting to bring McCoy's daughter Joanna in as a guest in some fashion. I'd probably nix the space hippie idea...
I'd let David Gerrold write another, more serious Trek story...
Yours, though, I have to say, gave me second thoughts... and it's the only post in this thread I could really get behind. Basically it amounts to "get the hacks and beancounters out of the way, give the really talented creative people behind Trek a free hand, and set them loose to make something even better than what we got." Hard to argue with that.