I assume that can't be a maximum pressure in the system either at high revs or at idle
The spring preload (by means of the washer thickness) will determine the maximum oil pressure at the pump
output [referred as (maximum) threshold]. When this threshold is exceeded a bypass will be activated between
the pump output and the intake chamber. Thicker washer will result higher opening pressure.
Until the maximum output pressure is reached, the delivered pressure will mainly depend on the (pump shaft) RPM
and oil viscosity (and of course the pumping losses).
With hot engine the oil pressure will be lower at the same RPM compared to cold engine,
(as you mentioned) and the pressure limit won't be reached below 5500 RPM.
So changing the washer of the regulator valve will only affect the maximum oil pressure,
below that the main limiting factor will be the pump delivery itself from the output pressure point of view.
Does that answer your question?