Odd Problem

To me, Sounds like Ignition or Timing. I would have leaned toward ignition with the lights thing, but you've already swapped out the ignition box.

Have a spare starter relay? They have some play on ignition, maybe swap one in that you know is good see if it makes a difference, but I dont think that would be it.

Where you've already swapped in a module, distributor, coil & other, I have to wonder about cam timing. Anything strange happen recently. How old is the timing chain? Think you may have jumped a gear?