Les Paul Junior - he borrowed Rick Ocasek's double cutaway for Blue then bought himself one, which was a single cutaway but still had the beefy tone. It wasn't quite as old as first thought (or something to that tune). I think Brian used it every now and then too, post green, though I may be wrong.
It's on the cover of the first Alone album, I think. Apologies if I'm wrong. The Blue Warmoth Strat was saved for live mostly as far as I can gather.
I've used a new Les Paul Junior (Special) fairly recently to attempt to gain a fairly similar tone, and results are good with either a Mesa, Marshall or AC30. I can point you toward such results if that's of any use.