You would need to add line chokes to the supply, and put some MOV units, 7N251, along with a common mode choke and capacitors, on the supply as well. Dropping R185 down to 100R will help slightly by removing charge from the trigger, but it will not help much. R182 and C80 are also wrong, drop R182 to 22R 1W and C80 to 100n 275VAC Class X, and duplicate again after the choke. That should reduce triggering, though the line chokes and input filtering and MOV units will do most of the work.