*** Please do not quote any of this message ***
You know what? It sounds like you really love each other. You can never resist each other, but you've got so much history, you've broken the relationship. There's little chance you'll be able to fix things, and wipe out all that past history to start again as the people you are now, not the people you used to be when you first met.
The only small chance you have is to commit to each other exclusively, put everything behind you (if you can), and work hard at making each other happy. The bad things will eventually fade into the past, if you can both let it go and be happy with what you have now and what you can build into the future. New, good memories can replace the old, bad ones.
If you want to be with her, and she wants to be with you, sit down, tell her how you feel, and see if you both want to give it a shot. If you're both dancing around each other saying that you still want to be single, but really just trying not to spook the other person, then get it all out in the open. Be honest, say what you want and what you need, and stop pretending to be in a romance movie where misunderstandings and the things not said to each other provoke comical/tragic outcomes.
If you really both want to be single and are happy that way, but don't want to be friends with benefits, then break it off now, and sever all contact. While you are in each other's lives, it's unlikely anyone will be able to make either of you happy. While you keep in contact with Sarah and she with you, your relationship will cast big shadows over any other partners either of you might find. She will always be a place you can end up for a while when a relationship gets to be too hard for you to work at. It will be the same for her. You are junkies for each other, and the only way to quit is to never do the drug again, even if you think about it every day for the rest of your life.
So make your choice. Go for it with her, pare the past away and start anew being the people that you wished you could be. This is difficult, but possible. You just have to let go of all the old baggage, and realise what you could gain with this woman you are so entwined with. The hardest thing will be not to fall into the old patterns that broke you apart in the first place, and you can only do that if you are the changed people you claim to be.
Or really start afresh, cut free from the past, including Sarah and all she represents, all she knows of you and the things you did that you now wish you hadn't. Leave her behind and move on, remove the temptation from your life so that you can go forwards instead of having her reach from your past to pull you back there.
What are you going to do?