OK, thanks. The coil is a 0.7 ohm primary resistance, which is about 1/2 of stock. Stock is around 1.4-1.6 ohms primary resistance. That is not horrible per se, but will cause the ballast to heat up more than normal.
I cannot find that ballast (Standard's old catalogs aren't online) but it may be a Chevy one at 1.5 ohms cold. Stock is 0.5-0.6 ohms cold. That does not sound like much but......
The ballast resistance will shoot up when hot; it is designed to do that. If you are starting with a 1.5 ohm cold ballast resistance, I have measured those to go up to around 6-7 ohms hot (with a stock coil), while the original type ballast will go up only to about 2 ohms. That resistance dominates over the coil's primary resistance and will set the coil current at about 40% of a stock ballast and stock coil. Since coil energy is proportional to the SQUARE of the current, the coil energy will drop almost sixfold.... and spark voltage will drop too.
But after the ballast cools (in a few minutes) then it ought to be back up there. So that does not explain all of the symptoms, but maybe some of the hot restart issues. (FWIW, it takes about a 30-60 seconds for a ballast to get to its hot resistance.)
Measure the ballast resistance cold, end to end, with one end's wiring disconnected, as follows: First, put the ohmmeter leads together and take a reading of the lead resistance alone; do that a few times and average the readings. Then measure the ballast with the meter and subtract the lead resistance. See what you have and let us know. The Mopar system uses an unusually low ballast resistance and that needs to be maintained.
The MSD ballast PN that 69_340_GTS listed above is 2nd best. The best ballast is an OEM Mopar ballast at the 0.5-0.6 ohm cold resistance range. Either may work OK with that low MSD coil primary resistance, but I would probably use the MSD ballast there. You that you will get as good a spark from a Pertronix Flamethrower 40011 with a 1.5 ohm primary resistance.
This may not be the whole problem but the wrong ballast would just make things worse.