I had the problem where the wires came out of the connector but were still in order so was able to use an eyeloop and tweezers to reassemble.
My HDD LED still works, but I don't have an IR remote to test with (I don't think the MacMini included one).
Any advice on testing the IR function?
Maybe buy or borrow a remote from an old Apple TV?

Ha! I had to do the steps TWICE since after putting the logic board in I could hear that thing rattling around.
Turns out I had flattened the upturned part of the clip during removal and pushing the board in would dislodge it.
There should be enough of an up angle so that the logic board clears the end of the clip and then holds it in place.

I am about to do this and saw your comment on the 'rubber washer';
the kit I have has rubber grommets that have to be inserted/snapped into the drive carrier holes first;

then the drive with the posts installed is installed so the posts rest inside the grommets

Or did you have a different type of kit?
(I see some with posts or with cap screws (Apple part 922-9584) or a combination of post and flat head screws.