How do I stop obsessing over my boyfriends past?

You want to save it, he doesn't. No matter what I say here, you'll just do whatever you think can straighten him out - us women are a little like that. It's not going to work out, hang on to your dignity and walk away. My ex had issues and told me time and again he'd quit but that was only to appease me. Do yourself a favour and find yourself again, then when you have that back - get somebody better than him.