I've tried adjusting my carbs and the idle speed to no avail. As the car warms up every time I come to a stop the idle drops well below the idle speed I've set and I have to use the choke to keep the car running.

Since the carbs work on air flow/vaccuume (I really do not know which) you might check your air cleaners - possibly a silly idea, but easy and cheap to do.

I would suspect that you have excessive wear at the throttle spindle / carb body junction. That lets in unmetered air and it becomes increasingly impossible to set a reliable idle. You think it's OK but it won't hold the setting as the spindle floats about. Not a cheap fix but it needs to be done right. Should then be good for many thousands of happy motoring.