The TL072 stages are the boost gain stage, a buffer, the clipping makeup gain stage, and a VREF buffer.
The trim pot is not in the feedback loop, in fact, it doesn't appear to be in the boost circuit at all, and that's puzzling me.
I have to trace the relay switching next to see how all of these sections tie together... I'm sure it'll all make more sense after that.
Normally I would have done that first, but since I can't easily remove the relays (there are three SMD relays in tight quarters) I'm saving that fun for last.