Dave,
I enjoyed the videos. Looks like a fun machine!!!
You may not be aware of this.... While the data plate on your Tucker may say "1542", the carriers on the machine have four idler wheels, which are 1300 series carriers. 1500 series carriers have five idler wheels, and their overall length is about six inches longer (76" versus 70").
I tried to get a good look at your de-icer wheels. Those are the rear idler wheels on each carrier. Yours are what I call the "modular style" in that they have replaceable UHMW plastic rings. My impression from looking at the first video is yours are worn out. The UHMW rings should be the part of the de-icer wheel that contacts the grouser track guides, but my impression is they are worn to the point that the rings are flush with the center steel plates the rings bolt to, so the steel rings are contacting the grouser track guides as well.
There's good news and bad news about UHMW rings. They are no longer available from Tucker. If you call the factory, they will offer to sell you some new de-icer wheels at a price that may have you gasping for air (no kidding). At that point I think your best option would be to get some new rings made from UHMW plastic. I know forum member Rob Miller has made some, and he would be a great resource of information on the how-to. The good news is getting new rings made will cost a small fraction of new de-icer wheels from Tucker.
I'm sorry to be essentially the bearer of bad news, but I thought you would probably like to know that information.