I like being on the same page.
So, maybe it's not Songverter that is at fault here. Maybe it's KHPro. Or maybe it's the key-changing software that you are using. Have you analyzed the original vs the key-changed WAV files?
Today, I will create a perfectly-sync'ed BIN file using KHPro. I will then split it into WAV+G and rejoin it back into another BIN file. I will post my findings here.