Mine is a '96 1500 and very similar if not the same. I would investigate the choke issue. In actuality, it is not a choke, but a fuel enricher. If the nut, you speak of, is broken, you might be getting a rich mixture when the bike is running. I would check that out first, before I went to something else.
The cold start problem............when you pull the choke out, I assume that the bike eventually starts, correct? If so, does it run at fast idle?
You might also check the bowl vent tube. It runs to a carbon cannister on some models and can give you fits. Try disconnecting it and running a hose, temporarily, to just down below the frame. See if the problem persists. A faulty cannister can sometimes increase the pressure in the bowl and cause the carb to run rich.
I am also wondering why the shop, that did the carb work, did not fix or at least inform you about the broken fuel enricher?
The cold start problem............when you pull the choke out, I assume that the bike eventually starts, correct? If so, does it run at fast idle?
You might also check the bowl vent tube. It runs to a carbon cannister on some models and can give you fits. Try disconnecting it and running a hose, temporarily, to just down below the frame. See if the problem persists. A faulty cannister can sometimes increase the pressure in the bowl and cause the carb to run rich.
I am also wondering why the shop, that did the carb work, did not fix or at least inform you about the broken fuel enricher?