Interesting, I've never thought of doing it exactly this way. Usually I see high surface area PIN junctions used to detect particle impact either by reverse biasing the junction or by directly measuring induced voltage. The amplification stage is not so easy. This is for particle counting and energy measurement though.
What kind of radiation are you measuring? Gamma I guess?
I guess the first thing that comes to mind is that for a given signal, as Vgs increases perhaps the on-resistance at a given voltage does too? If so, it might be easy to measure the voltage drop across the MOSFET on resistance and how it changes with dose.
If I think of anything else though, I'll let you know!
Edit: I suppose you could also use an R/2R network to provide an increasing voltage to the MOSFET base, and measure the point where the output reaches some threshold, a direct measurement of Vgs. That should be pretty easy using one full output port of an Arduino and one of the ADCs.