You really have no other option. She doesn't want to be with you and you have to respect that decision. Any contact afterwards just makes them more pissed off and angry. Even nice, friendly thoughtful things make them angry. You want to know why? Any kind of contact on your part reminds them of your relationship, the one that didn't work, and brings back all the things she was angry about. You aren't doing either of you a favor. You will always be associated with your past relationship and the issues. Plus when you aren't together, and you are commenting on what she is doing, it does kind of come across as stalkerish. Just a suggestion. The more you chase after her too, the more she thinks you need her, the more she thinks "Wow I was right".
You dated for a while, been apart for two years, and then back together and still it didn't work. And you say there were a few more on and off break ups over stuff you are trying to portray as not a big deal, but break ups are a big deal. They aren't (or shouldn't be) like moods, not like one day you feel like it and the next you aren't. They are the end of a relationship, and patching it up because you both hurt and lonely never solves anything. That is why inevitably it came to this.
You say you changed, and you want to prove that to her. Do you honestly really feel like you changed? Did you change for her or for yourself? What is so different about you? If you honestly feel like a whole entirely new person, you won't need to go out there and prove yourself. You will be satisfied with the change for your life because it's for the better and everybody that knows you will notice. But she won't get to unless she wants to. The only way you guys can truly create a new relationship is if she comes to you completely unprovoked and still has feelings for you. No matter what you say or how much you tell her you changed will affect how she feels. She will feel how she feels and her feelings can't be bargained with.
I'm not telling you to forget about her and move on, but if all you are doing is thinking about ways to get her back or doing things to get her back, you are fighting a losing battle. It's not looking good judging by how many times you broke up. You already failed in her eyes. Even if she does, you don't know if it would work anyway because she would need to improve too. Do you really want to be back with the same girl that had serious trust issues and give you shit for everything? Another recipe for disaster.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.