Carburetor/choke not working properly

It's a 71 429 with supposedly 70,000 miles.
I bought it a year ago, and had the stock (it's all stock) carburetor rebuilt, it needed it.
It ran fine for a few weeks.
Then it started to act up when cold started.
It flooded out, stalled, and blew out black smoke.
Took it back, and they adjusted the choke.

Turned out not to fix it, took it to another shop (I trust both shops) last week, they worked on the choke as well, drove it home, started it this morning, and it's the same thing, stalled out, black smoke.
But this is only when cold, when it warms up, it runs perfectly.
Any ideas?