Thanks for your help.
Morgan Dual 40 Clean, it's one of Andy44's profiles from The Amp Factory.
Guitar is a custom Telecaster, neck pickup, it's a Lindy Fralin vintage (so passive and low output, by no means I'm going to clip the input with something like this). Guitar is direct in the KPA. Clean sense is at 3.5.
Firmware it's the latest, 1.6, but I also tried to downgrade to 1.5 with no improvements.
I also tried system reset, flash format and reinit, reinstalling from USB. Nothing changed.
Had the same issue and solved it by using a full factory reset as per the WiKPA unofficial manual 'Tips & Tricks for the KPA (wiKPA) - For those who want to get to know their KPA far above what's in the manuals :)'
A&E
Make sure you do a backup first!