We'll never know the exact story on the Carson / Tonight Show thing, but I do recall Doc and Johnny Carson joking about Maynard and his "record label" one night while discussing getting more of the Tonight Show Orchestra music released.  I'm pretty sure they were confusing Maynard's publishing company for a record label, but Doc's line was something to the effect, "Well, if it's good enough for Maynard Ferguson..."  They both had a laugh, but who knows if it was "with" or "at" Maynard's ability to control some of his own business affairs.  Anyway, there certainly was some awareness of MF and his endeavors over at the Tonight Show camp.  The rest is all speculation.

Regarding Maynard's comfort zone, I do believe there were some situations when he felt out of his element, but I also believe that he went way out of his way to accommodate the egos of others sometimes.  That Dinah Shore gig is a prime example.  Yeah, Rich Little kind of shoves him off the stage, but throughout that appearance, and on the others with her and other TV gigs, Maynard goes way out of his way to acknowledge the contributions of the host and other guests.  He absolutely kills that arrangement of Something, then he bows to Dinah like she's Ella Fitzgerald.  That's just the man in action, I believe. 

Now, Sass and Brass was a bad idea all around.  Look at the performers on that stage!  They were all uncomfortable.  Honestly, Al Hirt comes off better than any of the other trumpeters, for me, but I think it had something to do with Maynard's presence.  Maynard had the decency to not go crazy with his range, and Hirt knows he can take Maynard on the intricate improve stuff and plays some tasty stuff.  Over the years, Maynard could have blown circles around a ton of players, but he frequently (and purposefully) did not.  Again, the man in action.

As for all the other gigs, some random thoughts: 
Arsenio Hall - Maynard seemed fine, at least as fine as he ever seemed fronting that High Voltage band, and he had some sidemen with him.  So, that one's okay.
Letterman - MF should have refused to do that without an on-air feature.  It's pointless as promotion if the TV audience does not see him.
Simon Dee  -  I've looked into these shows.  Unfortunately, the BBC was in the habit of recycling tapes and many of the shows were taped over.  Plus, at the end of the show run, apparently all of the remaining shows were bulk erased and all usable tape stock was returned to the general use stockpile.  That's a real shame.  There are a few trailers and snippets floating around, but so far no MF has turned up, sadly.  Ernie Garside seems to have some radio broadcast tapes, but oddly no TV stuff other than the show that Sleepy Night Records released, The World of Maynard Ferguson.  That's another real shame, as Maynard played the Dee show and a few others while living in England.