One thing I would try first is to validate that hypothesis.
Have you tried using a plugin that support half pedaling?
I encountered a similar problem with Arturia's Piano V2 piano plugin which got solved by setting (that plugin's inner MIDI setting's) controller CC64 mode from relative to absolute.
LogicPro 10.6.2, MainStage3.5.2
MBPro 17", Core2Duo, 8G, OSX 10.12.6
MacPro, Xeon 6Cores, 64GB, OSX 10.15.7
ULN8, MOTU MIDI TP-AV, C4, MCU Pro, KorgNano, Novation SLMkII
AAS, NI, Celemony, Spectrasonics, Korg, Arturia, etc...
PC, iPad3(V-Control & LogicRemote), AtariST(Notator SL), Several vintage gear