You seem to be saying they are both not interchangeable and compatible.
However, what I think you are saying is that there may be a CRT compatibility issue. In which case, take the Classic's "B" board compatible CRT with the analogue board to the Plus.
Since I have successfully powered all of the compact Mac logicboards with every other analogue board in some misguided experiment I was obsessed with, I will tell you that they are all interchangeable and will all fit within each other's cases. What is required in all cross-model utilization is a modified pin-connector cable, which is easily done by extracting the pin connectors from the plastic headers and inserting them into the proper order of the other Macs analogue connector. Keep in mind, the SE modifies its sound connection which requires additional configuration. Also, the Classic has software brightness only which is not implemented in other logic boards, so the Classic is not the best analogue board to use with earlier compacts for this reason (though I have never reduced the default brightness level on a Classic, if only because it was so difficult). This all works because the interconnect principle is identical on all of the compacts (excluding the CCs). The usual disclaimers apply ... I did not keep the logic boards connected in this fashion for any length of time, so long term result may vary.
That said, the board may be in better condition than you think. Perhaps Tom Lee can lend some insight as to why it chose to fry itself after it was powered off, though. Wile replacement may be the easiest, the time is coming where the working supply of replacement parts is in need replenishment, meaning this army should endeavor to repair rather than replace as much as possible.