Carpet padding often has a higher R-value than the carpet. 1/4" commercial pad is most often specified. Your choices are dictated by the heat loss of your room and the designed heat output of your radiant floor panel.

I'm already using a rubber pad with a low R value (0.45), but I'd like to find some carpet options that are low (relatively speaking).

This is not particularly low. I stay away from carpets over 1/2" thick and wool of any kind.

Again; Your choices are dictated by the heat loss of your room and the designed heat output of your radiant floor panel.

I would recommend something that is outside rated. They tend to be really thin and are meant to be used without a pad. I really would not put a pad of any kind under it; if you do you might as well not expect any heat from the floor, other then maybe a comfort heat and not any room heating.