The only way I think it would work would be if he stays living separately. If he doesn’t agree, then he’s just looking for somewhere to live.
Actually do it like starting again, but maybe have a type of contract or agreement about certain behaviours neither of you will accept from each other. How you will deal with disagreements, ie walking away, 10 min cooling down period?
How you will host each other, who pays what, take turns etc. Even what is expected on birthdays.
Think carefully about why you broke up, and put in rules about that. Write a list now of the poor behaviours that caused problems. Maybe even have a monthly review, either with each other or just yourself.
Remember Nothing changes if Nothing changes. Treat this like a work project, with expectations, management strategies, reviews and solutions. Expect your old relationship dynamics to creep in. Keep doing work on yourselves.
Read as much as you can about how good relationships work and how to communicate effectively. Put in boundaries early and be prepared to walk away at anytime. Just don’t drift into old habits. Do some therapy or enlist a friend to be accountable to.
Personally, I wouldn’t go back with my ex, but I’m not you.