Logic Pro - sustain pedal adjust

I hook up my Yamaha NU-1 to my laptop [both MB air and MB pro], hook up MIDI via USB, and run Logic with a EXS24 piano sample. Fine.

When i use the pedal while playing/recording MIDI, i half-pedal often. But even though i release the pedal fully, sometimes the MIDI info recorded is not 0 [completely released] but 1 or 2, which continues a [fairly heavy] half-pedal and blurs one harmony into the next.

I would like to adjust this in either Logic or my keyboard , so that anywhere near lifting my foot from the pedal is already recording 0 as MIDI info. The Yamaha, i can't find a way yet, and i am afraid it isn't possible.

Logic must do this, maybe by remapping the MIDI values in advance of recording. I have been searching but can't find a way to do this.

Please, does anyone know a fix?

I can of course manually adjust all the MIDI values in the edit window after recording, grab all those 1s and 2s and drag them down to 0. That is pretty tedious and surely there is a better way.

Any suggestions received with gratitude.