Most Helpful Guy
I'm not sure what I'd do, but I know the right thing to do is just drop the guy from your life. If he is hurting you like that, he is not worth your time. You don't deserve to hurt b/c this guy is too hung up on another girl.
If he doesn't want to stop talking to this girl and you're not okay with that, then leave him completely. Cut him out of your life. He'll come to his senses or he won't. But either way, you'll be free to pursue men who put you above all other women (except maybe their moms. :P ).
Additionally, I personally believe that going behind your back and talking to this girl even though he promised he wouldn't is probably emotional cheating. If he has a crush on her, (which I almost hope he does. Because if he doesn't, it means he through your relationship away for nothing) then he was absolutely cheating on you in an emotional sense. Which for some people, myself included, is almost more painful.
Most Helpful Girl
With an "EX" who may still Mark an X in his own softie spot here, dear, it seems that Knowing it could happen again, even behind your back, you will Continue having trust issues with him. And Knowing that he is 'Talking to any girl in the worl' and you are Not feeling the best about it, this will just go down a beaten path and always end up A... War of the Roses.
You have tried breaking it off but end up back together. And it appears that it will be nothing but a Full Circle Problem Pattern all way round.
You both need to sit down and have a serious convo about Getting on the same page. If you love one another, want to be two birds of a feather, I believe the past should stay in the closure closet and the rest of Not the best should Not be Part of any picture perfect Relationship you are both are trying to be in One nest.
If he wants to get up with this ghost and the Others he is talking to, tell him to leave you Out Of.. The picture.
Good luck. xx