Yay! You made it through this episode, and so did he.

Your plan to reach out next time is excellent!
I walked away, went in before bed and he said he hated himself was really struggling etc etc, then the breakthrough ! He admitted he knew I hadn't done anything wrong on Tuesday and was embarrassed and ashamed and didn't know how to rectify it. I told him a simple cuddle and apology for being off would have been all that was needed.
Buried in this is a subtle lesson that I've learned about the silent treatment, and what is going on in the head of a pwBPD... .and how/when to reach out.
It starts out with him being upset at something... .and taking it out on you with silent rage. Actively ignoring you, and sending you the message that you don't exist is horribly mean and invalidating... .and comes with a free bonus invalidation--if you call him on it, he can claim he's doing nothing wrong, and invalidate your very real hurt feelings about it!
The key is that it
starts that way. Even if what he's angry about has nothing to do with you, like he admitted it did.
At some point he transitions to feeling embarrassed about treating you so badly, and not knowing what to do about it. At this point, if he breaks the silence, he would be admitting that he did something 'wrong', and being a pwBPD, that would mean to him admitting that he IS a horrible awful person, painting himself black, and everything! Needless to say, this isn't easy for him to do!
The tricky part (for you) is that his actions don't change visibly when he goes to this second stage.
What you can do is find your compassion for the misery he's experiencing. I always believed that whatever abuse my wife was directing at me, she was always directing more and worse inward at herself. It didn't excuse the abuse, but it did help me find some compassion for her.
When you are in that compassionate place, and he's giving you silence, you can reach out gently in a way that lets him know you aren't angry at him, you aren't judging him, and you aren't pressuring him. That you will welcome him back when he's ready.
The key is to make sure that YOU are in that place where you can reach out without any expectation--you don't know if he is ready or not. He's not self-aware, but he is hyper-aware of your moods. He will sense your expectations and will react to them. Poorly.
I consider them to be little gentle 'touches'. When you are at home together, natural opportunities happen a lot--times you cross paths and can smile, or offer a cup of tea (maybe not--that could be triggering after the prior exchange!), or something.
If you don't get a positive response, wait a few hours... .or a day, and find another time where you have connected to the compassion, and try again.