Ok, I may be getting somewhere.
I tried re-assembling w/o the recoil spring, and it went on. It got caught for a second in the same place as above, but then slide back (quickly!) when I put a little force on it.
Is there anything obviously wrong with this picture?
It looks like the previous owner actually polished the outside of the barrel. Most of the barrel (except for areas I'd expect to see wear on) has almost a mirror shine.