when you’re following the exact same process on three other boards and they don’t display the same behaviour, you know the process works. The only explanation can be hardware. Putting that one module aside is about your only option at this point.
At the module level, you’re unlikely to be able to deal with a single component failure. About the only thing you could potentially do is replace the EMX module itself.
Throwing out this module sounds like a good advice, except that these modules are no longer produced and no longer available. So for me they are precious. That’s why I wonder what could possibly fail… and if there are some low level bootloader commands to deal with this situation.