Hi. I don’t have a QC but am interested in this topic. I get a similar experience (with my church) when using the NDSP plugins - headphones on my interface sound different to actual TRS → XLR output out the back of the interface - I always put this down to EQ difference in headphones vs speakers, but it’s a big enough difference that I don’t play with headphones because the sound feels dramatically different to me.
I wonder if a valid test would be plugging into your PA/speakers via the headphone jack with something like a TRS to XLR cable to do the conversion, and see if you get any notable difference - that feels like it would prove whether an EQ or tonal difference is happening for audio routed that way, or whether you are just experiencing a native EQ diff with your cans. You could compare that to coming from one of the TRS outputs on the QC also if you wanted to use the same cable. Just thought it might be worth a mention
Cheers