Sorry I didnt have this thread marked to notify me.
The circuit I drew assumed 20 mA LEDs for the resistor values I gave as an example. With high current ones you will want an emitter resistor of 0.6 / the LED current, as you found out. Say 1.8 ohms
The base resistor will need to be able to supply the LED current divided by the gain ( hfe ) of the transistor, which for a BC337C is typically 400, so would require only 1mA base current for your 350 Ma LEDs, say 5mA from the arduino to leave some flowing through the reference LED. ( one red LED at 2v is fine, and the temperature change will tend to cancel out the transistors change of gain with heat.)
So the base resistor should be no more than 3v / 0.005 = 560 ohms.