Right now you are in emotional dysregulation yourself. Like the intoxicated man who can't walk the white line, you can't clearly lay out two paragraphs - her reasonable narrative and your reasoned narrative. You are so completely focused on your narrative and so dismissive of hers, how can this go anywhere but down hill? If you need proof, look at the 100 conversations you have had.
If you want to make this better, you have to self sooth and get to baseline.
The narrative you have written above is not her position at all. It doesn't mention the lie (s). Surely that is at the core of this. I don't know what your narrative is but it seems like part it is "I haven't lied in __ weeks" this problem is over. As I said earlier, this is conflict is feeding on itself.
I can't really give you any specific thoughts because you are not being clear on what the opposing positions really are... so I can only make general comments.
Every time you counter her accusation that she lost trust because you lied with your narrative, you are invalidating her. When she says you behaved badly, let her say her piece and then say you appreciate her sharing and want to think about it and wait for her to shift the conversation or end it. Be ok with that.
Every time she goes into meltdown, stop and listen to her. If she get abusive, ask her to be respectful and you will listen. If she won't ask if you can pick up the conversation the next day. There is only so many words that can be said about what happened, let her get them out.
Don't swarm her when she dysregulates. Give her space. If she goes silent, let her go silent. Silence is ok. She will self sooth. She will return to baseline. She will call back. That might take a few days... be ok with it.
Validate the valid and qualify. If she says you are a liar. Yes, I lied about A & B. I'm ashamed. I understand why this upsets you. If she says you tried to replace her, I did get involved with x just like you got involved with y - its upsets me, I know it upsets you too. If I tried to replace you I'd be with her, right. If she argues, don't counter. If you are speaking the truth she will eventually self sooth and see your point.
You will do better to back off, be OK with ambiguity, take responsibility, know when to retreat, do not give her a bat to beat you with, and give her space to self-sooth and return to baseline.
That's an approximate formula - with more details on the narrative and other members input, you can shape it much better.
You probably want to deal with this almost the opposite of the way are pursuing it. That has a much higher likelihood of success
It will also help to consider that trust problems with people who have issues sometime can't be resolved. The best you can do right now is to create an environment where she can start working through her deep resentments on this issue. It's not the surface skirmish that you have that causes the problem, its that they surface skirmishes are triggering the underlying resent of being lied to.
Do you want to see this play out in reverse? Read this members file. Watch how the boyfriend plays it (denying her wound) and how she systematically responds (constructive and first, then bichy, then not constructively, then destructively) and how the relationship falls apart. You are on this path... get off.https://bpdfamily.com/message_board/index.php?action=profile;u=63476