If you are despereate put ferrite beads on both ends of any cables that go near the welder - and increasing the size of the battery can help as its a giant capacitor in effect and depending on the psu design it can help to smooth and absorb spikes other than that its filters and opto isolator time. The interferencce could be travelling into the panel via mains earth better deal with that too.

Had something similar years ago. We had a DA Ensign panel in a house next to a railway line. Now and again a spark from the electrified line caused the panel to go off for no reason. I fitted a mains suppressor kit from ACT, and 47uF caps from the zone + and - to earth, and ferrite cores ... Cured the problem, but it needed about 3 visits to do so....

To be honest, fitting suppression to a cheap panel is just adding the suppression that is removed to cut the panel cost in the first place by the manufacturer .

Get a decent panel, its cheaper than going back time after time under warranty. The client will just get hacked off, and the next company will just fit a better panel, curing the problem, making you look an amateur....