I did some experimenting and reading and this is updated circuit, there are no oscillations over what current range I can get (all the resistance in the wires with the crocodile clips add up to over an ohm), at least on the breadboard. I'll have to do some more reading on dealing with opamps in the future.

If this were mine (and a hobby) project, I'd just use whatever closest resistors I could get and did calibration of output I and V with the microcontroller software while testing the circuit. It's a lot easier to change few values from code than hunt absolutely optimal (=correct) parts. 
I think I'll put some more pots in there for the gains, but 1% stay, I've found the supplier that has them in stock.
Of course, there may be some accuracy loss, if the Op-amp gain/bias settings ain't just optimal for AD/DA conversions, but those can be fixed at next revision if you'll indeed need the maximum accuracy.
This is an experiment in analog/semi-precision stuff, I mostly played with digital electronics before.
And, wellcome the wonderfull world of electronics. Where lead times for even most mandatory parts can be 40 weeks or more.
I come from the boring world of software developement, where the bandwidth is the limit! And this annoys me like hell.

Hi,
Try a resistor of about 2.2K Ohms between the base and emitters of the driver transistors Q2 and Q4. With out this resistor the op-amp has to move 2x Vbe to before the gate voltage changes.
Tried it and no noticeable change in oscillations, just limited the maximum current of the sink.