Current Source - MOSFET vs Bipolar NPN/PNP for stability
Here's another topology to consider (found in many old application notes):







simulate this circuit &ndash; Schematic created using CircuitLab

You have said you don't want to discuss the voltage drop involved. So although that would definitely come to my mind in this design, I've decided to follow your lead and avoid thinking more about that question.

Aside from very tiny JFET leakage current, all of the load current flows through \$R_\text{SET}\$ and it is very easy to see that fact in the above schematic. You get most of the benefits of the exponential relationship in a BJT between collector current and base-emitter voltage changes, too, and the output should be quite linear with respect to the control voltage.

(I don't think you want the above, though. The following circuit modifies your circuit with Bode in mind. If you keep your approach, you should consider it.)



Let's return to your circuit. If you deal with a Bode plot, I think you will find this better:







simulate this circuit

I copied Henry's choice for \$V_\text{SET}=1\:\text{V}\$ in order to set your maximum current of \$1\:\text{A}\$. That impacted by choice for \$R_\text{SET}\$. But you can obviously change that as you see fit.

I think you should also review thoughts found in Linear's Current Sense Circuit Collection. There are a few ideas there you might also consider. In fact, the above circuit can be found as Figure 79, there.