Source Measure Unit Design Verification
From what you have provided, I don't see how your circuit implements a DAC to current source. I also don't see how you implement your voltage and current compliances. Going from your feature requirements, what you are presenting looks incomplete.

If you don't want to compensate for the voltage drop across your sense resistor, don't put your sense resistor outside the voltage feedback loop. Try putting the sense line on your voltage amplifier after the shunt resistor instead of before.

I highly recommend looking at the service manual for a Keithley 236 SMU. There is an excellent chapter that describes the theory of operation. The specifications are much more demanding, with multiple voltage and current ranges and significantly more precision. While many decisions they made are overkill for your needs, the way they handle compliance, measurements, and setting values is easily transferred. It may take a while to understand what's going on, but the education value is easily worth the time it takes.