Paul, Maybe you didn't use as large a screw as you could have, but one thing I've found that works pretty well, is to use the thin / fast CA in the holes. It really soaks into damaged torn fibers especially well in MDF, forming a solid plastic plug that will need a new pilot hole for the next screw. Otherwise, since I use the same line of 5mm holes for the adjustable shelves to mount the plates, I buy the mounting plates with those big fat screws already mounted in them. If you replace your mounting plates with these, I'm sure you won't have any problems, unless you have too large a door with too few hinges.
Just so you know, a 3/16" drill is close enough if you don't have a 5mm drill.