Yawn. I worked with 16 layer boards at a factory troubleshooting defective, new boards that cost over $8,000 to stuff. The internal routing of a simple low frequency board is irrelevant for drawing a schematic. You can X-ray a board or mill it one layer at a time if you want to duplicate the routing. All you need to do for bais reverse engineering is to trace each with an ohm meter by probing every pad and termination to identify the signal path and draw a schematic from your notes. I've done this with four layer boards for 30+ years. "Specs on the chips" makes things easier but knowing who made it, and how it's connected will tell you if it is a custom part or just house numbered.
There are industrial solvents to remove any potting compound, but they aren't cheap or easy to buy. Failure analysis is a specialty in electronics manufacturing. It is expensive but gives you the answers you need so you can design out the problems.
A jig to hold the module in a CNC machine would allow you to cut accurate holes down to the right points to see if the IC was bad, without unpotting a failed unit. Then a test fixture with 'Pogo Pins' would allow you to see what was bad. If there were enough bad units, it would be worth designing and programming a computerized fixture.