The assumed supply currents also involve 110 A GND return current. I think it's still in the normal range of backplane and power electronic PCBs. I agree with Mattylad, that copper bars routed to multiple press-fit terminals can reduce the PCB current density, but you may prefer PCB-only wiring.
As a first step I would estimate expectable bus resistances and voltage drops for different copper weights and number of planes and calculate the respective voltage drops. I guess, it will rather constrain the design than permitted PCB overtemperatures. Simple rule of thumb, 1 oz corresponds to 0.5 mOhm sheet resistance.