Use MOSFETs in paralel, just like you tried. But install a resistor from their source to ground. This will be the current sense resistor. Use an opamp to drive the MOSFETs. Have the voltage across the sense resistor fed to the opamp. The other input of the opamp will driven by a stable, adjustable voltage. That will adjust the current, because the opamp will always maintain the voltages equal. This will take care of all the non-linearities. As a reference I use a TL431.
You can parallel more than two MOSFETs, if needed.
Improvements to the circuit should include an undervoltage lockout: basically, the MOSFETs should be off if the voltage across them is less than, say, 3~4V. This will prevent you from turning on the power into completely enhanced MOSFETs, causing possibly the P/S protection to trip and making the load unusable. Maybe I will post that tomorrow.