Well, I see the obvious answer in Steve's original post big as life. You're trying to run laminators from a computer only panel! Of course they won't run!!
OK - seriously - this is a mystery. Here's a really long shot which should have no impact anyway, but is there even the smallest slimmest possibility that the new electrician wired the two new receptacles with H & N reversed? It shouldn't make any difference but you never know. Nothing else makes much better sense, and it's worth checking (descretely).
Other than that it would be interesting to hook up an oscilloscope to see what happens to the sine wave when the heater turns on. Try it using both the computer only panel and the other panel you mention (the one that works). It sounds like the laminator is causing the power supply at the panel to behave badly and then reacting to that by tripping the reset.
Radar
