Bowen,
I ran a die down the shaft of my side shift(S-shaped BT7, like yours) and found that a 7/16 NC(national coarse)14 fit well, with very little slop, even though the thread gauge prescribed a 16 thread size would be a best fit. I found the 3/8 NC16 was, in fact, too snug and I think it might take off some metal. That may be because the chroming process adds some metal to the shift stick and gives it a thicker profile. If you can find a 7/16 NC16 that might be your best bet. But If your threads are crushed or rusted, try the 7/16 NC14 first. You might want to wrap some teflon tape to give it more "bite" when you screw the shift knob back on. You can always take metal off later if this isn't a snug enough fit for you, but you can't put metal back on......
Cheers
Dave