Kinda "smells" like a defective condensor(capacitor)at least if it were on my 35 distributor.
Looking at your distributor photo again, it looks like that pin is way off to one side and hardly making contact. Perhaps the photo is of a different distributor?
If this is your actual distributor, then check the following . . .
Here is the area that Lawrie mentioned - the cotter pin looks loose and could intermittently be grounding out the points - which would cause this sort of issue:
View attachment 243764
Before you go crazy, try another coil. Beg or borrow one if you don't have a spare (spare coils and condensers should be part of your tool kit). The remote mounted coil like you have could not be easier to change. I have seen this problem before.
Just an opinion
Another idea hit me - how about the grounding of the engine to the frame? Do you have a dedicated ground strap from a head bolt to the firewall (or something similar in your year car)? If there was an intermittent or dirty ground, these types of problems can occur - especially with rust over the years.