Yeah when you mentioned the 'Popeye' thing I think that might help. If you make the puppet's forearm slightly bigger, that might disguise the puppeteer's arm more?
Also, you know know ya make that extra piece the same? [hard to explain, but If it's Ernie, the extendend piece of sleeve, which you shouldn't see, is the same as his shirt. Same goes for the extended piece for the bottom of a body of smaller puppets. Edit: 'Glove Tube', as you put it] Now I'm making that a dark, different material. Just a personal preference of mine, and I think it might help hide any little flash of the puppeteers arm on screen, or at least help with the illusion a little. Especially if it's a furry arm.
Just my $0.02.