Is the Quaverato the only thing in the signal path or are you still using your loop switcher? I remember when we talked last, that switcher seemed to have some weird things going on with it, so you may want to test the pedal without that in the signal path, if you haven’t yet.
I highly doubt that that the Quaverato’s voltage is the cause for the distortion. It currently uses 9 volts, biased to half supply (4.5V), so the signal would have to get pushed beyond those rails (+/-4.5Vpp) to distort. Guitar signals are usually much less than 1Vpp, so it’s very doubtful that an unamplified guitar signal would run out of headroom. Most likely, (if the distortion is happening internal to the Quaverato) the problem is related to an issue with the opamp (TL074) circuit. Check the ins and outs of those opamps to see if they are biased correctly around 4.5V. The schematic in the back of the assembly manual is useful for tracking down signal and voltage problems.
If you really feel compelled to use higher voltage in the Quaverato, 12V will probably be ok to use. The only thing to watch out for is the 5V regulator. If, after a while it starts getting hot, go back to 9V….I can’t remember off the top of my head what the max voltage differential (or wattage) that regulator can stand.
Good luck.
-Brach