MAKE SURE the points distributor has a GOOD "condenser" in it. Cheap to replace even if there is one in there.
(A "new" condenser does not mean "good.")
I would not run the engine for very long (5 minutes) without a ballast rigged up.
You should be able to "test bench" your points system by hooking up the following:
Battery/ clip lead---to coil positive, coil negative to distributor, distributor case to battery negative. "Rig" a spark gap, maybe even a plug and plug wire, from the coil tower to battery neg. (Ground) You should be able to TURN distributor by hand, even slowly, AND IT SHOULD make hot sparks.
They are cheap to buy at any parts store. If you have a Mopar electronic ballast, use that. If it's a 4 terminal, the two "halves" are different." Post back, I'll explain the proper way to use a 4 term. ballast with points.
I can NOT STRESS ENOUGH how important I believe it to be, to get your car running RIGHT WITH OUT the MSD stuff. It very well could be that it is introducing some delay in timing, or multiple triggers (false spark) that is causing part/ all of the problem
One more time, you should be able to "power time" the engine at a KNOWN degree figure of about 35* AND IT SHOULD RUN there with no more fuss.