no the reg doesn't control coil voltage, it controls current flow to the battery, so nothing to do with that
starters definitely drag down the battery so there's less for the ignition, that's why the bypass of the ign resistor when starting [12V], and the points dist wouldn't make a difference - I'd have the starter load checked, could be drawing way more than it should, the low volts to the coil is definitely the problem
Bill