Once the noise was present this morning, I pushed the A/C button while leaving everything else on and the noise disappeared.
OK, so lets suppose your A/C compressor (or clutch) is the source of the noise.
There are a couple of possibilities there:
1. The clutch itself is the problem (bearing going out, air gap incorrect, worn clutch surface).
2. The compressor is on its way out (or already knackered).
In either case, continuing to play with it can only lead to more damage.
IF your compressor (not just the clutch) is beginning to seize...then each time you run the unit...you are likely sending small metal particles though your A/C lines and components (hopefully most would be caught at the TXV).
So...best to stop using the A/C until you can have someone look at your vehicle.