Here are plots for the noise of my op amps (in Volts).
I compared 8 op amps, these are the two winners I came up with, AD743 clearly wins. I also included (for later reference) the noise of the ISS PDs I am using.
Op amps I looked at:
This list was made out of Frank's head based on what he thinks we already have. The AD743 seems to give a SNR of 1k throughout my measurement band, which was my somewhat arbitrary requirement (e.g. based on what I got optically when I used prisms, but I don't know how much my old layout was limiting me).