Update for anyone interested.
I tried swapping over the lines patched in to the desk, ran desk channel 19 down multicore channel 18 and vice versa.
Phantom was present on multi channel 18 but not 19, suggesting to me that the problem definitely lies along the cable run and not with the desk.
I reckon the issues must be with a connector either desk, or stage end.
It will be a while now until I have the chance to swap any connectors or take the panel apart, so for now it looks like I'll just have to avoid using that channel for a source requiring phantom. Not ideal, but manageable with our current schedule.
Unless anyone else has a suggestion that I can try in the meantime?