Attached is a simulation. I first tried an LTC Instrumentation amplifier, and it was way too slow. I built a Gain of 50 differential amp using a high-speed LTC opamp. It worked, but it was too slow, too. I then split it into a Gain of 10 Diff amp, followed by a gain of 20 inverting stage, and it works well. I made it so that it operates off a single supply. The rail-splitter (pun intended) is offset to allow for the asymmetric pulse. The floating voltage source at the input simulates what will come out of the delay line, a 3usec wide pulse.
The LT1215 is advertised as a "high-speed" opamp by Linear Technology. I used it in the simulation because LTSpice includes models for all of their products. I tried some slower ones, and they add a lot of delay, and their slew-rate is inadequate. These are pricey, but you will have to use an equally fast opamp if you are going to buy it from someone else.
I suggest you simulate the whole circuit, including the integrator. I have attached the ASC file so you can play with it...
btw- the title says gain of 50, but it is actually a gain of 200.