I've always been a very avid believer that coming to somebody and saying "I've changed, look at me" just proves that you haven't changed at all. If you have changed, you wouldn't really feel the need to jump up and down and say "Look at me! Look at how much I've changed!" I think it would be noticeable to anybody that knew you well if you really did change. And who knows you better than your ex girlfriend of 3 and a half years (which you probably knew for longer)?
You seem to be a very intelligent person and I have a feeling that what you are saying is genuine. You were caught up in that cycle of breaking up and getting back together, completely blinded to satisfying her needs, because you just wanted to satisfy your own: having her in your life. And that's why nothing changed, and it took really losing her and that feeling that comes with the realization of losing somebody for good to really get to the root of the problem. Which is you and what you needed to do to be mentally focused on providing for somebody you care about.
I can't begin to explain the similarities I feel to your story with my last ex. She wanted me to be spontaneous, to send her flowers (which I never did once), wanted to feel connected to me and the feeling of growing together towards something special. Which I dropped the ball on. Because when you aren't growing together, you are just stagnating. Love is alot of work, and above anything else, you have to be a consistent boyfriend. You might get a couple free passes if you have a stressful week at work or something comes up, but you have to ultimately keep yourself focused and keep yourself working towards something with her because those goof ups always add up and when things get bad, you better believe she won't just forget about them.
I think maybe part of your problem is that you simply don't know how to treat a girl. I know it sounds outrageous and ridiculous, I think we all think we have some idea of what a boyfriend is SUPPOSED to do. There is a huge difference though. I would be the first to admit I didn't know how, and I have plenty of issues in my life to back it up, but at the end of the day they are just reasons, and not excuses. And I think you have some idea now.
Keep in mind it's only really been a month and not much time has passed. I mentioned I believe in your sincerity but I find it hard to believe you have come very far. It takes some time and it takes some work on your part to make your every day life the life of a changed person. You know what you need to do to be a better boyfriend, but you could also be a better friend, son, brother, uncle, etc. Focus more so on those and as time passes I think you will feel better and better about your progress. You said it yourself you have some issues to work on, and you shouldn't be "working on them" while trying to redeem yourself with her. If you guys ever were to be together in the future, you don't want to be working on yourself, you want to be ready to go. A fresh start if you will with a whole new person, not a work in progress.
I know it's scary because every day you feel like you can lose her. And I'm not going to lie to you, you very well might lose her. There isn't really much you can do about how she feels, but you certainly can use this time as an opportunity to improve yourself. If she were to ever give you a second look in the future, you want to be ready. I wouldn't try too hard to keep in contact with her, but if she is keeping in contact with you, it's clearly important to reciprocate. You say you are fiercely loyal to her and love her to death, but keep in mind she also isn't the only one for you in this world. Use your options, and don't think for a second she isn't exercising hers. You might meet somebody else you don't have such a tumultuous history with and have that fresh start you are craving. But most importantly, it's putting your progress to the test. Because you will never really know how much you have changed until you are able to put your words and thoughts into action.
Just because you are dating somebody else (because she has already) doesn't mean you guys are doomed for good either. It would demonstrate your change to her and could be very impressive. You've already lost her, it's not like you are screwing things up any worse realistically. Not to mention it would help to pass the time which I'm sure is excruciatingly passing by right now.
I hope I've helped. Good luck with everything and I would be happy to talk more if you wanted to.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.