I figure this is the last opamp (buffer?) before the delay line goes to the resonance knob.
If I simply find a way to swap pins 2 and 3 of IC2 would that make the signal inverse?
Short answer,, NO.
longer answer; Quick fix mods without a deep understanding of how something works will just lead to tears.
Messing with pcbs is the fastest way to destroy a good working pedal.
If you want to fiddle with this circuit buy the parts and breadboard your dreams.
Phil.
In addition to what Phil said: you can't change the polarity of the signal at that point. It would upset the phase relation of the mixer in front of the BBD, as well as the mixer of clean signal and effect signal at the output.