Interesting - In the main interface in standalone, if you click an arrow above the velocity window, cycle to "Pedal" window and watch the green lines, to see if you're getting an OK gradation there (or at least 0 and 127) - BTW not talking about play-back of MIDI here, but testing your pedal. You might be able to see if it jumps all over the place, that it may be firing strange unbound signals instead of the expected smooth gradated ones.
After that, even if it didn't give clues, unplugging your keyboard (and/or pedal) and playback some prepared MIDI - to see if that has eliminated such errant firing on/off messages while you're playing back MIDI.
Just doing that might, at least at this time, isolate it to a hardware or just a loose connection issue. Some pedals can sometimes benefit from being opened up and moving parts cleaned.
Other than those things, I'm only thinking of things which may not really make sense on the face of it - but possibly try toggling 'Local Off' on your keyboard - seems a stretch but sometimes hitting that, or "Panic" (on keyboard or click the small round "!" button on lower right of Piantoeq's interface) can unclog some gremlin infested MIDI glitch.
Pianoteq Studio Bundle (Pro plus all instruments) - Kawai MP11 digital piano - Yamaha HS8 monitors