George -
Based on what you wrote, I think you may have a wiring problem between your Boss pedalboard and the church mixer. If you want a balanced signal out of the board to the mixer, you would use the left or both XLR outputs. The 1/4 outs are unbalanced, not balanced. If you built a cable to connect the 1/4 outs to an XLR on the mixer, you need a transformer in there or you won't be delivering a proper signal to the mixer.
Testing if this is the problem is easy. Use a regular microphone cable from your Boss XLR outs the mixer XLR in, or run a regular shielded 1/4 guitar cord from your Boss 1/4 out jack to a high impedance or line-level input on the mixer.
You didn't say which volume you were turning down when isolating the buzz problem - on the instrument, on the preamp, or on the mixer. I would expect the buzz would only go away when you turn down the mixer gain, but there may be a noise gate involved somewhere in the signal chain that could muddle the results.
With an unbalanced (regular) connection, the signal is the difference between the hot line and the ground line. If hum is induced into an unbalanced cable (e.g, gets through the shield), there's no way to reduce it since you can't tell what's your signal and what the noise is. With a balanced connection, the signal from your instrument is sent on two separate lines (+ and -) and the amplifier amplifies the *difference* between the two signals instead of an absolute level. These two lines are twisted together along their length under the shield (which is a separate conductor which is completely independent from the signal). The theory here is that if the cable is sitting in an RF field, the noise will be equally induced in the + and - signals, but when the amp takes the difference between the lines, the induced signal should cancel out completely.
A transformer is used to convert the unbalanced signal into a balanced one. That's what is in a regular direct box. That matching transformer will also normally play around with the impedance and signal level as well.
Without the transformer, it would be hard to build a cable adapter that wouldn't cause problems. You could put the unbalanced signals on + and - wires and connect the shield only on the XLR end and get something out, but the signal will probably be weak. If you tried to connect the XLR shield pin to the unbalanced ground too, it might hum less but you would almost certainly cause a ground loop, which would cause a different kind of hum. The mixer's ground lift switch might make it a little less noisy, but then you'd be back to basically running an unshielded cable and the original hum.
From your description, when you plug into an SVT, I'll be you were using a regular cable and not your Boss+adapter cable. That would be a quiet combo too.
Give the alternate connections a try. I'll bet that will fix your problem.
David Fung