I like the idea of using a flush cut bit to square it up but why not wait until you flip the unit upright, trace the square on the top of the hatch using the fan or the spacers as a guide, then cut 1/4″ inside the line. Then you can glue on the spacers using clamps with the 1/4″ overhang and clean it up with the router, rasp, or sand paper?
My concern with trying to glue it in place while upside down is that it will want to slide when you put the weight on it. You could probably put something in there to wedge it in place but it seems easier to use your clamps and give yourself a 1/2″ of play (1/4″ on all sides) when cutting the hole.
-mike