Rana suggested that I measure the OPA827 and OPA140 noise with high source impedance so as to see if we could find the low-frequency current noise corner. Below is a plot of both parts with Rs = 0, 10k, and 100k.
As you can see, both parts are thermal noise limited down to 0.1 Hz for up to Rs = 100k or greater. Given that the broadband current noise level for each part is ~0.5-1 fA/rtHz, this puts an upper limit to the 1/f corner of <100 Hz. This is where the AD743 corner is, so that sounds reasonable. Perhaps I will check with even higher impedance to see if I can find it. I am not sure yet what to make of the ~10-20 kHz instability with high source impedance.
EDIT: The datasheets claim that they are Johnson noise limited up to 1 Mohm, but this is only for the broadband floor, I'd guess, so it doesn't really say anything about the low frequency corner.
I have found two great FET input chips that rival the storied, discontinued AD743. In some ways, they are even better. These parts are the OPA140 and the OPA827.