With the rear wheel lifted I could sometimes start the bike with the clutch disengaged in the higher gears 3+. The wheel would not turn but once let go of the lever most of the times I could not disengage the clutch anymore and the wheel would keep turning...

Very strange, I'm left clueless to be honest. Could it be the oil, is the XT 660 picky about oil? I've used the same oil in my XT600E without issues.