Tap Tap Tap Sheldon. The screws are not really the problem. The real problem is the Tap. It is not economically feasible to have a special tap made to do just a couple of cues.
Again I disagree, if you can cut the threads you can likely also cut the flutes. One trick is to use the lathe carriage like a shaper (metal shaper that is). It is easier (and way faster) to use a mill. If you have a heat-treating oven they may even last a fair while, ie more than a couple of cues. Where there is a will there's a way. Home built taps are not that difficult really. I do appreciate that making one to perform a low dollar repair is often not a reasonable thing to do from a business perspective. I'm just discussing the ability to make the things.
I concede that if the lathe does not have gearing for a specific pitch then you are snookered, but some/most of the tpi numbers seemed common enough.
According to the threading chart from a South Bend lathe, one of the most common beasts around North America, it cuts all the pitches mentioned in this thread, including 7 1/2 tpi.