It really sounds like you guys can reconcile.
My husband, well we broke up (mutual) while we were engaged due to some difficult issues that was putting strain on our relationship.
We both slowly started to date each other again and ended up getting married about 8 months later. We've had rocky times, but who hasn't? It's been the best 7 years of my life.
Maybe instead of empty, awkward sex (b/c really what is the point?), you guys try for a romantic little date and see what becomes of it. Obviously, you are getting there anyways, why not communicate? It sounds like he's trying, maybe he is realizing what he's missing. Maybe you guys need a little bit of marriage counseling eventually and financial advising.
But, if it turns out he isn't interested, then really, the sex needs to stop b/c it's just going to be confusing and more difficult.