led - Make adjustable mosfet constant current source

I want to modify this circuit below so the current can be trimmed.

The problem is the variations in base-emitter voltage of the NPN transistor. According to datasheets, it is between 0.55V and 0.7V with a collector-emitter current of 2mA. I need to trim the current through the LEDs to 0.35A, using a potentiometer of 100 ohms or greater.

How could I modify this circuit? The supply will be well regulated.

^{simulate this circuit – Schematic created using CircuitLab}

Thanks

Answer

Do you have enough headroom to increase the current sensing resistor slightly an drive the BJT from a potmeter in parallel?

Of course you could optimize R3 to a series of resistors with ratios 270:100:180, where 270 is near ground, 100 is your pot and 180 at source.