The ICM grounds to the intake via the bolts, dielectric grease does nothing to help this. In fact dielectric grease is non-conductive. The heat sink compound you're referring to helps dissipate heat from the module. The intake manifold is literally a heatsink for the ignition module.
Sound odd? Chrysler used to put the whole damned ECU in the air intake ducts to keep it cool.
Okay now then, you replaced a module with one from a junkyard car because your fuel pump is on a relay right? I'm guessing you replaced the black box on the passenger strut tower right? That's not the ignition module. Look over on the intake manifold right behind the alternator and power steering pump. See the flat grey deal with plugs at both ends? That's the ignition module. 9 times out of 10, that's the culprit for what you're describing. A check engine light usually comes with this problem and a code check would show codes 223 and 224.
New modules are around $100.00 bucks. You might find one in a junkyard, but what are the chances you'd end up with the same problem?