Thanks so much for the detailed explanation!
I actually ended up switching to the LTC6268-10 and found that I'm able to actually get some semblance of a response from that opamp at my smallest pulse width. I am not trying to exactly duplicate the pulse; I am trying to detect that there is a pulse at all so I am thinking (hoping) that this is a sufficient response.
Here's the circuit?if you are interested in continuing to follow this saga. There shouldn't be any other files required except for the LTSpice circuit itself.