If it is capable of 300Apk, the forward voltage drop can be predicted by piecewise linear approximation above saturation.
A Silicon diode is usually saturated at 0.7V at Tj=25'C and any voltage rise above this comes from IR drop in the bulk resistance (ESR) related to it's size and thermal capacity. In fact ESR ~ 1/Pmax for the typical package design. The maximum current depends on the bondwire fuse limit I*t which be stated as a constant for a half cycle of line frequency or some other method.
Thus if the case is capable of 100W load with suitable sink, ESR is expected to be 10mOhm
Thus Vf= 0.7 + ESR * If
Testing at high currents is best done with a good CT to amplify the signal with low drop and good CM rejection of ground shift or equally good method.
Driving the device under test (DUT) with a pulse can be done by using an air core inductor shunting the diode such as 10 to 50uH from a low RdsOn source follower using a low voltage source with low ESR and "non-Inductive" wire series shunt to act as a current limiter from a low voltage.
the peak forward voltage and current is measured easily and when load is turned off , one can measure the reverse recovery time, and charge Qrr.