Optimizing op-amp overload recovery behaviour
Put 3 low-leakage low-capacitance diodes in series. Now, stick that in parallel with your feedback resistor R9.

When the opamp's output voltage becomes high enough, the diodes will conduct, and your 200x gain turns into a unity gain follower.

This will prevent the opamp from clipping, so it won't have to recover from clipping. It will not turn this slow opamp into a fast one though. You can always try, it is simple and cheap.