The LM338 will handle "up to" 5A. It does not mean you have to draw that much current. Based on that Youtube video, you can make a 1.6A current source with either the LM350 or LM338 with a 0.78 ohm resistor, very close to 3/4 ohms. You will likely have to use a combination of resistors to get the value you want.
The resistor should be rated at least at 2W heat dissipation in total, as it will dissipate that much heat. A 3W minimum to a 10W resistor would be best.
And, as chemelec says, you will need a heatsink for whatever regulator you choose.