single barrel carb problems

When you say 'choke plate', do you mean the jagged or stepped looking piece of metal that rotates on the side of the carb and that one of the idle screws rests upon? If so, that is the fast idle cam. There is a screw that rests on the 'steps' of that cam that adjusts the idle speed when the choke is active during engine warm-up; this is the 'fast idle screw' that it seems you have found.

When the engine is fully warmed up, that cam flips totally out of the way, which it sounds like it is doing. At this point, the car's idle is set by a different adjustment screw, called the idle screw, that rests against a non-moving part of the carb somewhere, and does not come to rest on the fast idle cam. It sounds like you need to find that idle screw and adjust that, it shoudl be nearby the fast idle screw.

Can you post a pix of the fast idle screw area? Or do you know if you carb is a Holley or a Carter?