12V 1A DC input filter
I have solved problems by doing things right:


Connected chassis to negative power supply lead where it enters the enclosure.
Ensured electronics insulation from chassis elsewhere
Ensured pieces of chassis are properly connected together
Will install Common-mode choke on power input to tame CM noise.


The problem was not with ESD, but with EMI (sorry for mentioning ESD at the first place). As the desktop supply is not grounded, it has +-160V 50Hz noise. When chassis gets grounded, massive voltage spike with huge dv/dt marches through the enclosure and gets coupled to all of the electronics inside. As a result, uC looses mind and reboots. With above mentioned measures, touching enclose with a grounded wire has no influence on operation.

Thank you for your accurate comments.