OK, then, check how well grounded it is! I recall when installing my after market one, the maker EMPHATICALLY insisted on a GOOD ground between the body of that ECM and the sheetmetal body. Use an extra bonding wire on one of the two bolts or big screws holding that module to the body, and run it to either the battery negative terminal, or another large grounding wire, like that near the carburetor return spring bracket or the firewall ground.
Do you have a simple 2 pole ballast resistor, or a double one with 4 connections? I suspect its a 2 terminal resistor. Is the ECM orange colored, or silver? If its an original Mopar box, its old. When cold, that resistor should be between .5 to ,8 ohms. DO check the impedance of the Edelbrock coil, though, as you say, since the problem existed prior to its installation, it may be matched well enough for a Mopar setup. DO check though.
Ideally, the hot resistance of your ballast should be about equal to the hot resistance of the primary side of your coil. This divides the coil primary voltage to about half of the system voltage, thus, prolonging the life of the ignition components. Of course, too MUCH resistance will result in poor spark, while too little will burn up the ECM. Note its temperature after a nice little 15 minute run. That will tell us much.