Speeding up turn-on and off with VOM1271 Photovoltaic MOSFET Driver (/optocoupler)

You can't get blood from a stone, nor high current from a small photodiode.

You could use a DC-DC converter to produce an isolated voltage and then use an isolator of your favorite kind (optical to logic, magnetic-transformer, magnetic GMR, capacitive) to transfer the signal and drive a fast multi-ampere gate driver (or possibly there are a few opto-gate drivers on the market).

A couple of the technologies I mentioned above do not necessarily have a known state at power-up so might be worth avoiding.