Ted,
A traditional method is to use the 'R' terminal on the starter solenoid to supply full power to the coil during a START. That bypass wire could either be attached to the coil + or it could be piggybacked on the coil side of the ballast resistor.
When the key flops back to RUN from START, it now supplies the coil through the resistor.
I would take a little voltage tester and make darn sure there was NO voltage to the coil when the key was OFF. Cooked points can make a car run poorly...maybe that's what going on with your rig. Check the points for any color change and take a look at the point surfaces..they should be smooth and shiny.
It almost sounds like your ignition switch is wired wrong and you have no coil power during START, but when it flops back to RUN it is powered. Powering the coil through the solenoid bypass (R) terminal would take care of that.
Stuart