ok... if the chips are all board mounted / solder then there is no "re-seating" and typically "solder-ins" don't have a problem.
Basically, when you lose PIP to the PCM, the PCM stops generating a SPOUT to ICM which causes things to stop firing which cause other things.
Your question about the "response" to heat and then die as it cools / runs is tough because we don't know the exact nature of the "thermal trace". As you have found, letting things sit for a "long while" assuming totally cooled to ambient air temp, allows you to start and run for some period. Then as the circuit works which I assume brings on a degree of heat causes the circuit to "soft fail". Heating to a "cosy temp" allows things to work fine. I don't know... lots of possibilities I guess... transistors, IC's to some degree, capacitors maybe, and even resistors... but ultimately, I still feel it is a cracked track / cold solder which is a good "thermal type trouble". As the board or component expands during use, the expansion difference from non-uniformity of heat (ie some areas / components are cool while others are hot ... by large resisters / transistor with heat sinks) puts stress on things. "Uniformly" heating "everything" may result in greater expansion overall such that connection is never lost from the smaller "non-uniform heating areas".... I don't know.... I think this is like one of those "I know **** when I see it" things. I will give you an example... take a resistor, as it operates, it heats up, this causes the resistor to "grow" in length... it puts a stress on the two attachments... if one of those points has a problem and "lifts" just a bit or it cracked, the expansion forces might be just enough to cause a loss of connection and you go from there. However, with your "massive heat blower", the overall board now expanded probably a lot more than the expansion of the individual component and thus that "massive expansion force" prevents any circuit "breakage" and you have no problems...
...:-(
If I had the module in front of me, I could probably narrow things down better. Do you have any electronics friend that can take a look at things a bit now that you know a bit more about the failing operation and circuit flow????
OK here is another idea to help try and sectionalize things. Maybe you can build some form of "air dam" (card board or something) to block the heat / air from say half the board and then try and see if you can find an area that will help a no start condition, turn into a start and run. As you see, I am almost running dry of ideas.... sorry... but my head hasn't given totally up.
PS... those IC's on the side of the case sound like transistor packages and are using the case as a heat sink.... you might want to aim at those specifically and see if that helps.