I can't tell you what to do, I can only talk about myself here.
I think that monogamy is an unnatural idea that causes me to split mind from body. My body wants one thing and my mind has been trained to shut that down because it isn't right. That basic self-deceit will cause me to do a lot of self-destructive behavior, over-eating being one of them.
The answer for me was to remove the idea of monogamy all together. When I did that, my reasons for having sex with a woman or relating to people in general changed immensely.
One of the big changes has been an awareness of my own body. I pay attention to the underlying emotional dialogue between myself and another person by 'listening' with my body instead of just listening with my ears. This has everything to do with having open, honest, and loving relationships which are a prerequisite to fulfilling sex.