I'm happy to report that when I isolated the Omni that it was dead quiet with the CIOKS DC7.
So it appears it could be a patch cable (unlikely - it was quiet before i added the Omni, the cables are brand new, and I've swapped a few things around already and haven't been able to resolve it) or a "doesn't play well with others" situation. If it is an other(s) situation I'll have to try and alleviate it by changing pedal order or some other possibility.
So I'll ask this, where is everyone putting the Omni? At the moment I have it:
bass>dirt(multiple, only use 1 at a time)>Omni>Solarian>Super Stack>S1>amp