~40 uA current sink... what current mirror topology to use?
I came up with a design that satisfies me enough to build and test out... it's of the hybrid approach where there are dual emitter degeneration resistors but of different values. Here's a picture of the circuit in a little test fixture in LTspice:


The idea of the test fixture is that it should pull about 60 microamps from a 2000 ohm source. I didn't simulate any of the op-amps, just this particular bias network thingy. So the current sink ends up lowering the voltage at the output node between R3 and R5, rather than raising the voltage at the op-amp output, but it should be similar enough.

Here I've hooked it up to a "PULSE" voltage source which goes from 2.5V to 2.4V... This is similar to the input to my system. I really only care strongly about the DC accuracy, os this is a good test. I'm aware of how awful the piecewise-linger PULSE waveforms are, but I figured it'd be fine. Here is a shot of the output current and voltage waveforms. It's showing the input pulse voltage waveform on top and the same voltage waveform at the node after the 2000 ohm resistor (i.e. between R5 and R3) below. Also shown is the current waveform through R3:

Not bad! I think it's good.

Now let me put a 10ns edge in and see what happens. I'm not expecting to have anything this fast but let's try just for fun:


Well it's wrong by basically 50% at peak, and the error lasts like 50+ nanoseconds, but evidently it smooths out the edge at the output node and gives it this RC-like appearance. I'm okay with this! My circuit is really slow.

Now, with the dual emitter degeneration resistors I think the accuracy will be good enough with the nonmatched dual 2N3904 package, though I don't know how to test this with LTspice. Best of all, I had 47, 470, and 30k ohms resistors in my "standard parts," (as well as the dual 2N3904), so I can implement this circuit at very low cost in the larger system. Great! I will try it out and hopefully it will work well. I'll try to try it first with separate 2N3904s which I'll choose to be particularly poorly matched. Hopefully the output current accuracy will still be okay in this case. If so then I'll know it'll be as good if I use the dual 2N3904.