How we did it years ago with big concerts, especially those that had large choirs was this. Invert the phase of 1 or 2 mics in a group of mics. say, in the choir, 2 of 6, for the front vocals, 1 of 3. This is where those phase invert switch in mid to large consoles come in handy. if you do not have that feature, make a phase invert connector. its like a very short mic cable with pin 2 & 3 inverted on one XLR.
Phase cancellation is prominent in the lower freq. region, not too much at the top. The other thing is, you are not giving the mic exactly the signals anyway so there would be very few points where a frequency would cancel out.
I don't subscribe to the idea of inverting the monitoring, logic being, if you invert the whole lot, it would still be, in essence, in-phase (all moving in the same direction) It may be out-of-phase with reference to the Front-Of-House and that all together would have an adverse effect on you sound….and yet not really addressing the core problem of controlling feedback.
1) Check speaker placement, is there a mic that is in front or near proximity to the main speakers?
2) Is the feedback coming from the monitors or from the FOH?
3) Are the right mics being used?
4) There might be too many mics open at any 1 time.
in any case, this might be a bit crude but if you feel you have done everything and the feedback is still there, you could experiment. While the service is going on and there is feedback, flick the mute switch one after the other (going off-on) if the feedback disapears on a certain channel(s), then that is it. I suggest the MUTE switch as opposed to riding the faders up & down because if you are using Pre-fader on your wedges, it won’t get affected whereas the MUTE kills the channel.
Just pick the service with the least people so that when they start noticing, only a few heads with a frown will turn to you…..hahahah