I've tried peg compound. Doesn't work.

The problem is that using 12-string guitar strings on the cobza is a relatively recent idea, and while the instrument is plenty robust enough to take them, the Romanian makers at Hora Instruments haven't modified the mechanism to match. They have also probably cut a few corners to pump up mechanized production - very old cobzas don't seem to need the machine-tuner hack that the younger Hungarian players use for their Romanian factory instruments.