Sounds like you have all of the electro-mechanical stuff covered pretty well. The only other thing that I could think of that would affect both the Lincoln and the Hypertherm is the air supply. How dry is your air? Do you have sufficient volumn?
I have a DHC Plasmacam with a Hypertherm Powermax 1000 and when I have problems, it's usually a ground or my UPS. I have my Computer, monitor, pcam controller on a UPS with power filters on a seperate circuit. Sometimes the UPS needs to be cycled or I get some wierd symptoms. Time to get a better UPS