In that case, I’d probably not worry about switch bounce, depending on whether a change of Performance messes with the chord ‘hold’ until the next chord. Mind you, from the front panel, changing inversion seems to be not dependent on another chord coming in at all. But yes, it does seem to wait for the next NOTE in the bassline before it changes.
I rather sidestep the whole issue myself by generally playing a full keyboard part for the first verse and chorus in Pianist2 mode, which naturally gives me the correct inversions (while I sing the head) and use the chord sequencer to play the solo sections so I don’t have to input any chords at all or worry about their inversions during solos or improvisations. Even the most basic two handed chords can drive the arranger while keeping the bass inversion correct.
But I still think the two opposite polarity ganged pedals should work to go momentarily from one Performance to the next and back. Have you tried it yet? There are plenty of tablet style footswitches that are switcheable polarity and quite cheap.
https://www.sweetwater.com/store/detail/KSP20--on-stage-stands-ksp20-keyboard-sustain-pedal for instance. Just glue or Velcro something hard across the pair to make them both work at the same time, and build an FC7 DIN plug to 1/4” female jacks converter….
Push comes to shove and you end up not liking the system, you can always retask them to other useful FC7 functions like Leslie fast/slow or MFX on/off etc..
The Performance can store far more than OTS can, I still think it’s your better bet and will dramatically reduce your having to navigate around to call up custom styles.