I hadn't thought too much about the Muppets truth be told, but that's a strong way to lead it for Henson. The Muppets going over to another company is entirely possible, especially since Nelvana ITTL are trying to go for quality above all and be what Disney isn't. This might just come back to bite them later on though.
Henson is far more than the Muppets, actually. The Muppets were his big break and as of the time of his death still a money maker, but by the mid 80s he was ready to move on to darker , more mature stuff. In addition to the continuing Muppet movies and the Muppet Babies cartoon (the latter a HUGE hit and merch-money maker OTL) and Fraggle Rock, Henson put out The Dark Crystal and Labyrinth, neither of which was a major blockbuster, but both of which made modest box office and which have become major Cult Classics, (particularly the latter with Bowie and his memetic package). Look to both for examples of when "quality" is put before "marketability" in the OTL 80's, BTW. The late 80s saw him attempting to move out from under the Muppets, hence the negotiations OTL with Disney that resulted in the sale following his death, and into more "mature" fare. His life-long goal was always to get puppetry out of the "Age Ghetto" and recognized for the high art it is. Jim Henson Tonight saw the Muppets return to TV, but also wicked-awesome gothic things like The Storyteller. This was the era that saw the rise of the Creature Shop and Animatronics (Henson's company coined the phrase and the shop to this day remains at the forefront of the art, as well as being involved in some of the earliest practical computer FX). Upcoming OTL things included creature/alien effects for The Empire Strikes Back and Return of the Jedi as well as Dinosaurs, the first animatronic "live-action" sitcom, which was a moderate success. Even after his death the Creature Shop has been behind some of the most epic practical effects in Hollywood (The Fifth Element and the TV sci-fi show Farscape demonstrate their work most obviously, but they're behind a lot of movie FX you'd never know).
Sesame Street will continue pretty much as OTL, I imagine, with Henson and Oz handing off the reigns to Kevin Clash et al. Butterflies could potentially limit Elmomania (simply butterflying Rosie O'Donnell's TV show and subsequent Tickle-Me-Elmo madness following her endorsement OTL will do it), though Elmo's sheer charisma will ensure plenty of success ATL. No Elmomania would limit funds for Sesame Street, but save the character much of his OTL hatedom. Fun fact: when Henson worked for Children's TV Workshop in the 70s he was friends with and worked alongside veteran screenwriter Tom Whedon, whom he'd worked with before. Whedon wrote for Electric Company. Undoubtedly Henson, Oz, Juhl, etc., knew Whedon's children, Joss, Zack, and Jeb.
Henson was in the process of a move towards the type of dark, fantasy-based stuff that had he lived would have been right in time to ride the Goth wave of the 90s (another fun fact: Tim Burton worked for Henson as a background muppeteer before he began his stint at Disney). He and friend/co-producer Jerry Juhl also were always looking to do weird experimental stuff like A Tale of Sand, which recently appeared in comic form but was intended for a movie (arthouse/Sundance stuff; little mass-market appeal).
ATL I can see the rise of Nelvanna as an alternative to Disney. He could work a sale or license agreement for the Muppets with them when Disney starts giving him the runaround. I think Nelvanna would actually USE them too, not just bury them like Disney did OTL lest anything upstage the Mouse. Potentially Henson could eventually get "bought" by Nelvanna and left as an autonomous entity as per Disney-Pixar. That would suit him well as it would enable him to pawn off a lot of the day to day business and marketing work and concentrate on his "art".
Whew...sorry for the novel! I never know when to shut up when I'm geeking out.