Differential input voltage necessary for maximum slew rate in operational amplifiers
Usually overdriving the input causes longer time to exit from saturation. Note that slew rate is not closely tied to that time, and some op-amps can lollygag around for 50usec or more before deciding to exit from saturation. 

I suggest you use an op-amp that is specified for your (ab)use such as the AD8067. That particular one might not be suitable for you (gain must be >= 8 for stability) but the time to exit from saturation is specified and it is reasonable (~200ns) with significant overdrive though. 

I don't think I would trust the SPICE models to necessarily model saturation recovery accurately. It could be a lot worse than the simulation would imply, so verify by testing.