Ah, OK I see what you mean now, but I'm not sure this is a solution to my problem -
first point is I want a transconductance stage, by which I mean I need any current between 0-10A under control by an input voltage. 0-5V in -> 0-10A out. What you are describing is timing a particular rise/fall time to get a certain current. All that would be affected by temperature coefficients in the diode, FETs etc. Unless I'm missing something and you're implying some feedback control circuitry somewhere..
second point is that if you're turning the current source off in the steady state, haven't you just made exactly the same problem for yourself again? How is the current source which turns off in steady state any different to the original problem?