Exhaust smoke after 5 minutes?

I'm fixing up a '76 Chevy Malibu with a 350. Until a month ago, it had sat
undriven for about 3 years. Before that, it would smoke a little at startup
then would be fine. I figured it was valve seals.
Recently I've unclogged the PCV valve, replaced/reconnected vacuum lines,
put in a new battery, and changed the oil which was black and seemed very
thin. I also changed the plugs, which were all oil-fouled.
Now that it will start again, a few things have changed. It now doesn't
smoke at startup, and idles smoothly, unless I put it in gear, then it
generally dies until I get it warmed up, then it'll keep running in gear.
After about 5 minutes, then it gradually starts belching blue/grey smoke
from the exhaust.
My guess is that somehow over the 3 years it sat, oil got into the
exhaust/muffler and doesn't start smoking till all that gets hot. Does that
sound possible? If it was just valve seals I'd expect smoke only at first,
and if it was piston rings, I'd expect smoke all the time.
I'm guessing that if I ran it long enough it'd all burn off. But after a
few minutes it really clouds up the neighborhood.

Any thoughts/suggestions?