One of the difficulties in using a torsion balance to measure G is in knowing the properties of the torsion fiber to a high degree of accuracy. There is another torsion balance method, called the frequency shift method, that reduces this uncertainty. The balance is allowed to oscillate freely and the period of the oscillations are measured. I think I would use this method if I were going to attempt it. You could get very accurate timing pulses from a GPS receiver.
Because of the difficulties in measuring the force of gravity, G is the least precise constant in all of physics. You may find this website interesting:
http://www.npl.washington.edu/eotwash/experiments/bigG/bigG.html