Best I've managed so far is 3 out of 4 pins. The 4th is at least 1mm off and there's no room to push the drive further, nor can I bend out the mounting bracket any further than I have.

The drive seems fairly stable, but the mounting bracket won't fit back into the case with that one corner pushed out.

Too tired and frustrated to deal with this further tonight. Giving up for now and, realistically, probably will need to give up permanently. Nothing I can do if it physically can't be done.