People are different. I think it's unfair for you to dictate who she may be in contact with just bcoz you break off contact or you're insecure. Just bcoz you don't notice a beautiful woman when in a relationship doesn't mean everyone goes blind. And just to clarify, appreciating a pretty face is not the same as lusting after somebody else. You know, I had a bf who tried that stunt, at 1st I thought, 'it's ok, I can do this' but then I realised that cutting contact with my ex lover was of no benefit to me, it just fed his ego. We're friends to this day, and that was 8yrs ago! My point is, it's unfair for you to choose for her. AND she HASN'T even responded to him. So again, I don't understand why you're stressing bout him being on a contact list...
If this relationship is for keeps, then her ex lover is not even a factor, bcoz as YOU clearly stated, they only hooked up inbetween relationships, which means he's not a threat. No crime in them hooking up in the past, they're 2 consenting adults, they didn't cheat on their partners, wether it was healthy or not is not the issue. Please stop imposing your will on her, THAT is unhealthy. You will ultimately push her away.

Best of luck to you both. Hope it works out for you guys.