It looks like your driver uses a resistor to sense current, so I'm not sure why relays/MOSFETs are being suggested? Such are usually a last resort when switching very large currents. The LED driver datasheet says the resistor sees 1/400th the LED current, which is 1A max, so, 2.5mA sense current if my math is correct. I believe the Arduino handle that directly (<40mA), no?
So, why not go back to your original idea of using PWM, but use a suitably large capacitor on the analog pin to smooth 99.9% of the ripple out?
Alternatively, why not just use two sense resistors in parallel, and switch one or both on and off directly with one or two Arduino digital pins?
Admittedly, I am an Arduino and electronics noob, so if this is stupid please explain why so I can learn.

Thanks,