Get your coils rebuilt from a pro, being sure they have been adjusted for current amp draw on a hand crank machine or Strobospark, that's the only way to get coils to fire with intensity and no double sparks.
If your mag is good, your coil box good, wiring good, and timer in shape, then rebuilt coils is the way to go.
A dizzy belongs on a Model A,......... Henry made 15 million T's using the magneto/trembler coil ignition.........this system works when you expend a little effort and a few bucks, rebuilt T coils, new points, new condenser, and tested right run about $50 ea. and will last you years and years with no maintenance