I don't know why one bank is hotter.
If the throttle speed adjust screw is backed all the way off and it still idles at 700rpm, then some possibilities are:
The throttle is hanging open, maybe caught on the gasket, maybe stuck in the throttle bores of the intake or spacer.
The secondary throttle is adjusted too far open.
Vacuum port without a cap
Vacuum leak.
Some other means of getting air into the intake.
Since the engine runs with the mixture screws all the way in, you need to fix that. Anything else will be only a bandaid on the problem, which could lead to far more expensive problems, fuel washing the cylinder walls, oil dilution, etc.
Fix the idle speed problem and idle mixture problem and then move on. Maybe they are the actual issue, too.
Another thing is that your '56 312 requires a '57 or newer distributor to work with the Summit carburetor. I don't think that would cause the hot bank issue, though and it would not cause the idle speed and mixture problem.
Lawrenceville, GA