is it possible linear response photodiode amplifier using 2n3819
3kHz is pretty pokey.
Maybe establish two separate feedback paths for AC and DC  using a couple BJTs for the DC path, with the  usual R and tiny SOT parallel C (for stability) to control the AC gain. Add a pole in the DC feedback to isolate it, well below the 3kHz (maybe 10Hz).
Early voltage will limit the maximum value of AC feedback resistor R.
Preferably run the PD in reverse bias mode to a negative supply rail to minimize capacitance.