I doubt there is really anything you can do about the opinion of the Hollywood producers.  They are always going to err on the side of caution. 
 
You are correct that the copyright is on the character and not the style of puppetry. It is going to be difficult though to get any character that has any similar traits past a companies legal department. If you have a pig or frog character they are most likely going to shy away.  Even a big furry monster is going to be a hard sell. 

It might help some when you run across this with a producer to educate them some. Show them examples of hand-in-mouth puppets that predate Henson.  Give examples of other puppet companies that use hand-in-mouth puppets that are successful. For example, Alf was created by Paul Fusco not Henson yet he could have been mistaken for a Muppet. 

Also never use the word Muppet to describe your product.  They are hand-in-mouth or hand and rod puppets.  I realize you know that but wanted to put it here for others to benefit from. 

Thanks for that Shawn. It  is comforting to know that at least we are clear on the  actual legality of it all, even though  Hollywood ignorance, and therefore opinion, affects  things drastically. Educating producers is a task. I ran across  a major one here in Colombia once, almost got a meeting with him but flaked when  he asked if I had heard of '31 minutos' of Chile. You might not have heard of them, but they were/are  Chile's and therefore South America's  biggest puppet  hit of recent times. If this guy does not consider that we would automatically know about 31 minutos, he really has no clue and will not take us seriously.  You are right, I never use the word ' *uppet', and I refuse to do copies of their characters for anyone that  asks ( I did do a miss Piggy once, for a friend, and it was terrible anyway) 
   Unfortunately  it is not possible to register  puppet characters with  the Copyright Ministry here in Colombia, as they are behind the times and do not recognize  intellectual property copyright. They consider a character is an 'idea' and therefore not  copyright. Forget the fact you spend a lot of time and energy on  design, and make patterns, etc, A drawing of your puppet is copyright protected, but  not the puppet., nor the character. Here you are free to make anything you want with Micky mouse  Miss Piggy and Kermit, as those characters are only 'Ideas' in Colombia's eyes. Step out  of  Colombia and you  die in the  courts for doing that.  I have been considering  if  you could  take out  patents on the patterns for  individual characters. ??   Anyhow, thanks for the comment. Solidarity is a good thing. I will keep you posted on how things go..

Its not Muppets, but there is a similar area of contention with Jeff Dunham. He has kind of slacked off on it in recent years because of the negative press he was getting with the ventriloquist community, but for a time there, he/his attorneys where bringing cease and desist letters, threats of law suits and a few actual filings against any ventriloquist that had an old man puppet. If he felt in any way that you were copying Walter, he would get his lawyers involved, even if the puppet didn't resemble Walter at all. 
The thing with copyright and trademark is that you can't copyright or trademark a concept or idea. It has to be fleshed out. With a puppet, its the same as a graphic design, illustration or  cartoon character, as long as there is a 15% change in the appearance and you aren't using the same voice then legally it falls under derivative works and you should be in the clear. Same reason you can see Calvin and Hobbs knock off stickers on the back of vehicles peeing on things and a jacked up Mickey Mouse flipping someone off. 
The real problem is the fact that Disney has their sticky little fingers in the Muppets. They are one of the top three most litigious corporations out there and they really don't care if they win. they have so much money that they just keep you tied up in court so long that you go broke trying to fight them and then they win by proxy.