One Frogboy's Opinion (and it is just an opinion)
After many successes, Jim Henson had finally started to lose some of his touch before he died. The Henson Hour just didn't work to the benefit of fans, the material, the Muppets, the network or even Jim it appears. Labyrinth underperformed and he just couldn't wrap his mind around why that happened.
American and global tastes were changing and he was figuring that out. I think Jim would have his fingerprints all over the internet, technology and...I think he would have had some deals with Pixar. Jim was very interested in animation toward the end of his life including Muppet Show characters (not as babies) in an animated feature.
He just wanted to create, and create things away from the Muppets. He wanted Disney to handle the property and just pop back in when a project rolled around, make his tweaks, perform and move on to non puppet or fantasy projects.
Muppet Christmas Carol would have happened, but it would likely have been a little lighter and different. Treasure Island is anyone's guess. I think Jim would have liked the idea, but not to follow Carol. It would have probably come later. Muppets From Space either wouldn't have happened or it would have been an entirely different film. We all know that he'd have respected Jerry's script.
Muppets Tonight could have happened. I think it would have played very much like the Henson Hour with Kermit in the background and I still think it would have had some trouble. Pepe would be around. Bill Barretta was a friend of Brian's so I'm certain he'd be working with Jim and the Muppets and have his Pepe character, but he'd be reeled in a little bit more.
Jim and Eisner got along. Who knows if it would have lasted, but Jim had a way with people. Remember that Jim Henson would be turning 72 this September. His pace would have naturally slowed down a little. He would basically have had his own production company under Disney's banner to do with what he pleased. This would have likely included:
Numerous fantasy films and TV projects
Attempts at live action/non puppet fare
Muppet TV projects and films
A Muppet animated film
Internet technology projects
Theme park attractions with the Muppets and Fraggles
Likely Fraggle and other cable projects for Disney Channel
Sesame Street, as a separate entity from Disney, would have Elmo and many of the newer characters of today but it would remain an ensemble. There would be no Elmo's World. Frank would have likely left Sesame and the Muppets anyway (first in dubbing performances then eventually like today).
Anyway, from the bits and scraps I have learned over the years this is where he seemed to be going. The Muppets would always be around, but Disney would maintain them so he could do everything he'd always wanted with his own healthily funded production company.