Wow, so I think I might've found something out about the show.
So I was poking around archive.org when I found this puppetry reel of this marionettist named Phillip Huber who is apparently kind of well-known in puppetry circles because he worked on Oz, The Great and Powerful:
https://archive.org/details/PhillipHuberPuppetryCareer. If you look around the 0:04 mark, there is this marionette that looks suspiciously like the marionette from the Peppermint Park segment "Red".
I then did a Google search of Phillip Huber, and this video came up:
Based off these two videos, the two marionettes pretty much have to be the same as they look identical.
So basically the question now is did people know about this guy's involvement at all or not, because I've certainly never heard him mentioned. Also, don't know if the guy has died or not; and also, if the "Red" segment was produced specifically for Peppermint Park itself or just a stock segment they just threw in there. (I'm betting the latter, but you never know.)