I would substitute the Pteronix back to points & condenser, certainly would eliminate the ignition.
Was this problem gradual or overnight?
If carburetor does what its suppose to do when cold, i.e., step on gas pedal, choke plate closes and a shot of fuel gets squirted, and there is no vacuum leaks (cracked hoses, broken vac modulator diaphargm if auto, all intake gaskets in good shape as well as carb -to-manifold, etc.,) it should start with relative ease, once again, providing piston ring seal is in good shape in order to create good starting vacuum.
However, with electronics, it either works or it doesn't, not this middle of the road stuff.
Could be fuel pump not working to its fullest capacity.