There has been a number of how to’s to get the screws to line up when re-inserting the exhaust fan,
I like to adapt things I have around my house for that.
here is a screw guide using Heat shrink tubing
Measure the tubing to be flush with the hole, trim off excess,
put shrink tubing in hole
push screw into place, and gently insert fan onto post, then tighten screw
You, my friend, are a genius! And something like this that every fan and like devices should have. There are lots of things like this that have holes for screws that are impossible to line up.