Had the same type issues with my big pontiqc and edelbrock carb. Manual choke and auto. Once it was running but still cold it was real touchy to find the right place for the choke to sit. In out on off it was never happy in one spot for more than a minute or two.
Finally called edelbrock and they said its normal and offered a new linkage that would give me better control. I decided to buy electric choke it worked like a charm and never needed to touch it again. Just got the kit plugged it it and weverything worked. From the first turn of the key. Also noticed choke would be working for several minutes after the engine was warmed up. And always adjusting a lot more than i wanted to try to do while i was driving or sitting in the drive waiting for it to warm up.
After the electric choke i could start the car and run back in the house and wait til the rpm went down and new it was warmed up and have heat. Before i had to sit and baby the car or floor it out the drive way to keep it running in gear. It was also annoying in summer with the manual choke.
Get the electric kit and be done. You will be happy you did.
Fix the fuel leak asap. Small problems can get much bigger if not corrected right away.
Dont screw up the tune of your warm carb if it runs right. You can try some more timing but you will be taking it back out come summer. Best to reslove the issue not the symtoms.