Be careful going deeper. You may not have enough meat to grip or you could crack the case if you force it too deep. The hole could be conical shaped and your measurement would be slightly deeper then you can tap.There are three options, in order of preference:
a. Tap deeper with the existing size and use a longer screw: easiest. Measure the depth of the bore with a piece of wire, and compare to the stock fastener length. If you've got 3+ mm of usable bore past the stock screw length, go to the longer screw.
All I'm saying is be very careful as you go forward to make sure it is all done logically.
Good luck.