I'm trying to say that's it's not necessarily something wrong with your equipment. I'm saying that GFCI's can "false trip"...especially less advanced ones...and would be most likely to do so at power on when you start out with big surges of power.
"Excessive lengths of temporary wiring or long extension cords can cause ground fault leakage current to flow by captive and inductive coupling. The combined leakage current can exceed 5 ma, causing the GFCI to trip."
Harrison County Rural Electric Cooperative Nuisance Tripping
"you mention the facility has motors, pumps, compressors,
etc. and there's some implication that maybe the power
line fluctuations / noise from these may be relevant
in causing the GFI's to trip."
Ground Fault Isolation Text - Physics Forums Library
"A GFCI is subjected to tests that simulate long branch circuits. While there are no specific rules concerning the length of the circuit protected or the number of receptacles on the protected circuit, remember that the GFCI will add up all the harmless leakage currents and capacitive leakages. Under extreme circumstances, this could "preload" the GFCI and make it appear overly sensitive or, worst case, result in nuisance tripping. Therefore, you should minimize the length of circuits to the degree possible."
Think like a GFCI
I would buy a new/more advanced GFCI...otherwise...call an electrician and ask him if that's normal. Have fun.