Ok, here goes...
It sounds like you are making some genuine efforts toward repairing your relationship. Other than wHat you have been trying, the one thing I encourage you to do is give it time. It sounds as if she still cares about you and is around enough to see improvement. You just need to make sure there is improvement to see.
The first thing I would do is make sure she understands just how sorry you are. I know you have already told her. Tell her again, but also tell her you understand her hesitancy in accepting your apology. Tell her you aRe making changes and you hope in time she sees those changes. After that, back off and give time and change a chance to heal.
Then start making the needed changes. Become financially independent. Work hard, pay your bills on time, and save money. Take better care of yourself health wise. I am not sure what this means, but you are. Do what needs to be done. Last of all listen better, I believe as you make the other changes, the opportunity to do this one will present itself. Honestly, if you make the other changes, you prove you are listening already.
Last of all, be patient. It took years for you to reach this point. It may take years to repair it. If you push her, you push her away. You admit you deserve her separation. Do not argue otherwise. I have confidence you can repair this marriage if you follow these guidelines. Just give it time.
My one last pointer is seek individual and couples counseling. If she is willing, find a way to make it happen. if you had cancer, you would find time for treatment. Your marriage is ill. Seek the needed treatment.
I hope that was helpful. Let me know if you have questions.