Controversial Option. Apologising for causing an a

[MrBond]

"My previous apologies when she left were pretty much that I was sorry for whatever it was she claimed I did.
Sadly, I ended up trying to defend myself all the time. Not attractive."

You're missing the point. This has nothing to do with "attraction". If you were wrong, then you were wrong and you should apologize. But only apologize if you truly mean it and understand what you did wrong and are actively trying to change to correct those mistakes.

This is not a ploy or a strategy. If they aren't sincere whereby you aren't going to make these changes for life or will slip into old habits, then she's not going to come back.