I think your system probably has a Ground Fault Protection relay (GFP), not a GFCI. A GFCI trips at 5 milliamps for personnel protection. A GFP can be set to trip from about 30 amps to 1200 amps.
But the setting is not the problem. As long as there is no ground fault on the elevator circuits the GFP should not trip at any load. If there is a fault there would be a lot of smoke, so we could assume there is no ground fault.
More likely there is a wiring problem with the ground fault sensor or a faulty sensor. Maybe the neutral CT is connected backwards, or not connected at all. Maybe all the phase wires are not centered in the sensing CT so the high inrush to the elevators is not accurately measured. Or maybe the GFP relay is one of the bad ones that sometimes trips due to saturation on high currents or harmonics.
If the elevators have modern VFD based controls, the harmonics might affect the GFP relay. This usually is a combination of 3rd harmonic currents in the neutral and a reversed neutral CT connection giving a false trip signal.
Another possible problem is improper connection of a neutral bonding jumper downstream of the GF sensor. An incorrectly placed jumper can shunt neutral currents around the sensors so the phase and neutral currents do not add up to zero, causing a false trip.
Bottom line, thoroughly inspect the ground fault installation and find the problem, or that main will continue to trip. Just raising the setting is dangerous.
Excessive ground fault trips on a Bolted Pressure Switch can wear it out, leading to a switchboard burn down when the switch contacts no longer fully make up. (This happened some years ago on two projects I was hired to repair.)