'The lies, the deceit, the humiliation...'
Right, so this guy has proven himself to be completely UNtrustworthy time and time again. Yes?
So common sense tells you (and indeed anyone with more than half a brain cell) that to trust him would be a bloody stupid thing to do.
So you don't.
That's it I'm afraid. There's nothing you can actually really DO about it! You aren't MAKING yourself distrust him. You can't simply CHOOSE to feel inside that he is trustworthy. It just IS. Is he trustworthy? Based on everything you know, no. He's not.
If it changes, it will do so over a long time. Because to genuinely trust him again your brain would have to say 'Yes, I really do think, based on many instances of him proving that he has changed, that he is now an honest person.'
You could pretend to trust him, of course. That's essentially what he's asking, with the rather manipulative 'leap of faith' bullshit. It's essentially saying - 'Yes, I fucked up, but I'd rather not have to be the one to live with the consequences, because it's inconvenient and feels bad. Hey, I know, why don't YOU get to be the one who feels bad? Yes you - the one who didn't do anything wrong. We'll just carry on as if I'm perfect, with me getting to not have to reassure you and prove myself and maybe give up things I enjoy and maybe still have the opportunity to fuck around , and you get to live on your nerves, worrying that you're being taken for a ride, worrying over what I'm doing, waiting for the axe to fall. Because that's easier for me, and I'm the most important one. More important than you, anyway.'
Your 'inability to put the past behind us' is also known as not being born yesterday.
His nagging and sulking is a better sign than anything else that not only has this waster not changed, but that he's too lazy and entitled to even bother to want to make it up to you.
I'd give him the boot, myself.