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Op-amps can be tricky things to spec. Almost all op-amps that their output slammed into a rail will take some time to recover. It is best to avoid that situation by clamping the inputs.
If you need high gain then it is usually better to use more than one op-amp is series so that the gain is distributed. When a lot of gain is in one stage then oscillations can become a real issue.
A good op-amp is from the OP27 family, there are several newer and improved versions of this op-amp offered by several makers.Some other op-amps that may fit your needs are: ADA4898, LT6230, AD8021, OP2177, OPA827.
Increase the analog PS voltage to keep signal away from the rails.If at the point of going digital you need it fast at the digital rail, consider a comparitor (which are designed to be fast at extremes).
Good luck, and please let us know how it goes.
I'm building this sensor for the "masses". Hobbyists, who are creative and don't want to pay the the big bucks companies.