I think others will tell you DANGER! but in theory you can swap in a 1.44mb drive briefly for emergency diagnostic reasons. In theory there's a controller incompatibility - I think. Someone else will do a great job tearing me apart for this suggestion, that will probably contain more detailed technical info.
When I first tested my SE/30 box (the logic board is in indefinite triage), I put my (800k) SE board into the case and connected the floppy. I only used an 800k disk but it read correctly and ejected when I shut down. If you're out of options and/or want to try, that may be an option if you have an unambiguously working 1.44mb drive. I'm not sure if your symptoms could be the result of a controller problem (on the board itself).
When I first tested my SE/30 box (the logic board is in indefinite triage), I put my (800k) SE board into the case and connected the floppy. I only used an 800k disk but it read correctly and ejected when I shut down. If you're out of options and/or want to try, that may be an option if you have an unambiguously working 1.44mb drive. I'm not sure if your symptoms could be the result of a controller problem (on the board itself).