Issues with 74 Dart

Dying when shifting from P or N into R or D is usually symptomatic of a lean idle, as is having to rev the engine. My 69 Dart slant was like that for years until I finally got a good rebuilt Holley 1920 carb (~4th I tried). It also liked excessive advance at idle.

I don't quite understand the "only when you move back to run". That can happen if you aren't getting IGN2 powered while cranking, which happened to me when I wired only IGN1 to my new electronic ignition. It would fire as I released the key (IGN1 gets power only in "run" I found). However, you say you verified that you do get spark while cranking. Perhaps it is a weaker spark when cranking. Is is possible it is mis-wired so that the ballast is active in "start" and bypassed in "run"? I hope the problem isn't in your key switch since those are a pain to change in a 1974.