The correct thread in the lower is SUPPOSED to be 1/4" X 28, as 1Gunner mentioned. Whenever a screw seems to start, then stop pretty fast, it may be that the screw is incorrect. This happens often when a metric (6mm) screw is used by mistake, or perhaps a 1/4" x 20 is used.
Get a 1/4" X 28 tap and clean out the hole, and ensure you have a true 1/4 X 28 screw. Most hardware store screws are 1/4 X 20 which aren't correct. Go for a socket head cap screw instead, which are readily available in the finer pitch.
If the hole is completely buggered, you can drill it out for a 5/16"... use the correct drill for a 5/16" tap, then go ahead and use the tap. You will probably have to open up your grip hole a bit.
Check the screw. BM doesn't often do shoddy work, and I suspect the grip threaded hole is done via CNC and/or a tapping head, neither of which is known for a buggered thread.
Good luck!
edited: Sorry a lot of this post doesn't apply to you as you have already cleaned up the hole, but I'll toss it out as general advise for others!