Tried getting some Lego tires to replace the ones on Beachcomber and Rukus. I have no idea if these will or won't have the same plasticizer problem down the line, but it was worth a look.
The 61254 tires are a decent fit for the rear/shoulder wheels. They don't fall off, but they're not snug, and slip loose after rolling a bit. So I may need to try and check if poster tack or floor polish or super glue would help them stay in place. Of course I'm leery about experimenting with even more substance reactions.
Also, the thing is I forgot that the wheels were different sizes. So now I'm trying to find some 50861 tires locally for the front/knee wheels, and also have a handful of the bigger ones I don't need.