It sounds like he feels genuine remorse for his behaviour, but that he thinks he can fix it by waving a magical wand of good intentions. I think you know, that won't work.
Promising to start therapy soon is not the same as actually starting therapy.
I think fixing all of this is beyond the scope of advice on the internet from random strangers. It's going to require hours and hours of intense therapy for both of you, individually and as a couple, to get to the bottom of all these problems.
If he is borderline and/or bipolar, he may benefit from cognitive behavioural therapy and/or medication.
One thing you can be certain of is that he's currently stuck in some patterns and he can't get out of them just by wishing it so. Lying, retracting promises and agreements, manipulation to make you seem like the bad guy... just to name a few. You may want to take some steps to protect yourself emotionally and maybe even physically (financially) from those behaviours.
Mental illness can "snap." It can lie like a sleeping dragon for years, and then be triggered literally overnight by nothing in particular.
I'm not a professional and I haven't met him obviously, but his behaviour does sound consistent with some forms of mental illness. If it runs in the family, that makes it even more likely. I would be strongly urging him to seek professional help, probably a full psychiatric evaluation.
The rest of this post basically assumes a diagnosis of some kind.
I disagree that all those behaviours are "who he is." Brain chemical imbalances can make people do unbelievable things, and take them away from who they are and who they want to be. You can completely lose the ability to control your actions. It doesn't make him a bad person. It makes him someone whose brain has been taken over by the wrong chemicals, neurons misfiring, sending mixed messages, delivering signals to the wrong place.
Sometimes, just having the diagnosis and understanding where these behaviours come from can go a long long way towards coping with it. My mom is Type I bipolar and she goes into pretty severe manias. After knowing her long enough (my entire life, obviously, but only really understanding the disorder in the past 5-10 years), I can now tell just from her emails and phone calls when she's in a mania or a depression. There's nothing I can do about them, and really not much she can do about them either except weather the storm, but I find that if I point out that it seems like she's in a mania or depression, it helps her come to grips with her thought patterns, and be careful not to make any rash decisions (especially financial).
One thing that really helps me cope is to think "This behaviour is not my mother. This behaviour is my mother's disorder. She's under there somewhere, and her suffering during these episodes is a thousand times worse than the effect on me."
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker