I just had the same problem, mine turned out that the ground cable to the battery had disconnected itself in the leaded fitting for the battery post, changed to a new cable and all the problems went away......
Currently running mallory dual point YL dist, can`t get points for them aymore, but they still sell the dist/dual point, (don`t figure) anyway if I convert this dist to a unilite, I`m assumming that the ignition harness would remain the same? Rick