how can you be sure electrical attraction is not interfering? I understand those forces are much stronger and might have contributed to the balance moving.Short answer: I can't. I'd be sure it was electrical if the masses repelled. I did the experiment in a humid basement during the summer rather than in a carpeted room during a crisp, dry winter, but it's hard to discount electrical attraction.
Lincoln Quirk did the math and came up with a value of G = 1.32 * 10^-10. That's good enough for me (and sounds near what I came up with, but my memory might be fooling me).
I remember the most difficult part of figuring out G was determining the angular momentum of the torsion balance and deriving the restoring force from the period. I had my physics and calculus textbooks, but they didn't give the formula. In fact, the textbooks had this particular configuration as one of the student exercises. I eventually set the problem up as an integral and solved it, but it was a bit painful. (It's not a hard integral, and it's not a hard problem, but when was the last time you did it?) Our local library didn't have very many of the kind of reference books you'd need for this. Inter-library loan works great if you know the title you want, but it isn't as convenient for browsing. The monks at the monastery down the road were in the middle of illuminating Strunk and White and were expecting to take a while before getting to anything scientific.
Thanks to everyone that wrote in!