I think the most important thing to consider when casting a Muppet adaptation is the jokes. With that in mind, I think this is the funniest possible casting.
All of the hobbits except Sam, Merry, and Pippin being frogs is funny. You can do a meta joke about how they needed some way to cast some of the classic muppet characters in this one.
Animal as Gollum shouting "PRE-CIOUS PRE-CIOUS" is perfect.
Gonzo the Grey just works. And the eagles being the chickens is obviously funny.
Rizzo is at his best when hanging around making meta commentary about the story as in Christmas Carol and Treasure Island.
Need to keep Aragorn a handsome human actor because Ms Piggy playing Eowyn and crushing on him will be all the funnier.
Ms. Piggy playing both Galadriel and Eowyn is great because you can joke about there not being many significant female roles in LOTR, and then you can turn that back around on there not being any female muppets either.
Keeping Faramir and Boromir as humans will be way funnier when Pepe is just relentless tearing Faramir down, and Faramir playing it straight and caring very deeply about it will be a lot funnier.
Statler and Waldorf should obviously both play Saruman together, as they did with Jacob Marley.