If I remember right, the purple wire is only for starting. It supplies power to pull in the solenoid of the starter. It has nothing to do with the distributor. The key switch sends power out by way of the purple wire only in start position. The "R" terminal on the solenoid is to supply power to the coil when in the start position. If this wire is not connected, it won't start, UNLESS you have the coil wired direct from the fuse box or some other sorce. With HEI its best to hook the feed wire directly to START and RUN at the key switch and run a single 12 gauge wire to the distributor. Just jumper across RUN to START and see what happens.
My guess is when you screw driver start it you are back feeding 12 volts up to the key or fuse panel. Thats the only thing that can be happening if you do not have the "R" terminal hooked up. This second wire "R", was GM's way of getting full 12 volts to the coil in the start mode. Once started the resistor wire from the RUN circuit knocked the voltage down to 9 or 10 to keep from burning out the points. They found it was to hard to get them to start with lowered voltage.
For the random acts of not starting, could be a weak moduale in the HEI and its acting apon the voltage variances when starting. You could still have a questionable connector someplace.
If you are running the HEI through the bulk head connector, you may want to rethink that and hollow out one of the holes to feed a direct wire out. HEI likes full power, the more the better, and each connection you have will reduce that voltage down.
Joe