As the person in the world who is the worst at soldering, I would say let's just try my luck with some connectors.^^

I remember wirewrapping being a thing a while ago 😀

I happened to be working on a CDROM today that had the same sort of connector that I salvaged (actually a pair of them) from a dead CDROM to use with the USB backplate years ago. The spacing and size are correct, but I had to trim and file down the plastic to make a pair of them fit on the pins.

Thanks.
There are suitable 2.0mm USB brackets. One less problem. The PS/2 mouse connection remains. The pins for this are not on a line and must be connected individually. There are 2.0mm to 2.54mm jumper cables, but only two-pin. Three of those and it should work. Not pretty but doable.