I think it's difficult to work both AA and RR at the same time, because they really are based on diametrically opposed philosophies.
AA's philosophy is that the individual is powerless over alcohol and therefore requires the intervention of a Higher Power in order to recover.
RR's philosophy is that the individual has the power to quit and is quite capable of doing so once an irrevocable decision to quit has been made.
I think most of us find that we "fit" within one of these basic viewpoints, so from my perspective the thing to do is go with the approach that best suits you.