Carter BBD Help
Right, timing too far retarded can cause no idle.
However the BBD is known to plug the idle fuel pickup tubes. That's the part inside the primary venturi held down by 2 screws. I'd suggest pulling the carb to remove those, otherwise you could lose a screw down the intake.
Pull the assembly off the top of the venturi cluster and inspect those two tubes that drop down into the float bowl. they have to be open and not clogged or won't idle. The way it sounds now, it's only idling because you have it cranked far enough to get into the main metering circuit instead of the idle circuit.