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Yes, I had previously attempted the center route.

Yes, I meant I failed enough that I'm no longer in fight mode. I had the jacket on.  I don't know if this helps, but I tried taking the jacket off and putting it back on again, and I noticed that, first, the bunny suit had been added to my inventory early, and second, changing outfits in any way played the "I can't change now it would blow my cover" dialog that I assume is only meant for trying to take off the street clothes while try to go the prostitute route.  Getting caught again didn't work, unfortunately, but going back to an earlier save did.

Trying to get broken Mezz through district one but whenever I get to the tunnel area it says "I should get my clothes first" even though I already found his clothes.

Once you unlock the VIP room how do leave it and go back to the game? I can't find an option for that anywhere! Do I just have to go back and not unlock it?