If I understand correctly, you're looking for 720 detents per revolution. The encoders I use certainly wouldn't do that, but I would question whether your pot system would either. But with a normal encoder of, say, 30 detents per revolution, you could simply define one detent as representing whatever 0.5 degree represents, and it would take multiple revolutions to represent 360 degrees. There is encoder software that changes what a detent represents depending on how fast the knob is turned. So if you turn the knob slowly, each detent is one step, but if you turn it fast, each detent can be 10 steps, or 20, or whatever, depending on how fast you turn it.
This video has code like that:
https://www.youtube.com/watch?v=2IQFX-KgTpk
Well, I don't know what you're actually controlling with these pot changes, but generally an encoder will give more precise and reliable steps than a pot can.