Static electricity flows between potential differences and it does not matter if ground or not. You can get shocked touching a metal doorknob in a wooden door and few of them are grounded... The argument could as well be made that you should get a worse shock with a solid ground due to the lower impedance.
The dedicated lines (circuits, runs, whatever you prefer) should have included a good ground return (neutral) and safety ground. If the electrician did not do this he violated code.
Does the voltage dip when measured at the service (panel, breaker)? If so your main feed is inadequate (or something is wrong in the HVAC, possible but unlikely). The ground return has nothing to do with voltage sag (unless it is seriously miswired; the ground is a safety ground and should not in general carry large current). It may be as simple to fix as putting the HVAC on one side and sound system circuit on the other leg of the incoming feed.
You might consider putting the low-level stuff on an APC (or whatever) UPS to protect from power glitches. The power amps will probably ride out short ones and it would cost a fortune to gte UPS' big enough.
No way would I risk myself and a lawsuit for the church (and me) by doing it myself. Grounding the sound system, maybe, but not for the electrical circuit. I do not know code in your area, but am surprised a 24 AWG service ground passes...
Seriously, you really need to have a licensed electrician deal with this. Anything else is a huge liability for both you and the church. It sounds like you have already decided to jury-rig it so why ask?
Whatever - Don
"After silence, that which best expresses the inexpressible, is music" - Aldous Huxley