Jenny, it sounds like you and I have similar partner types, so I can empathize with the confusion and hurt you may be feeling... .In what I used to call his "Stonewall Mode" (before we learned his diagnosis and I began learning about BPD and understanding that this was not actually punishment with forethought on his part) my guy could spend weeks without speaking, emailing, or smoke-signaling an unessesary word... .holed up in his home office with the door closed, refusing to communicate even for critical work purposes or regarding important social invitations, and even wearing headphones (sometimes even obviously disconnected ones) when in common areas of the house to make sure it's clear he wasn't only not speaking to me, he wasn't listening either! It was absolutely brutal. He is in inpatient treatment now and we are barely starting to address how to move forward with our relationship/communication, so please take that info into account with my response: I'm no expert nor success story.
I'm not sure if I can offer you what I think you're looking for, which is a concrete solution; and I think most on these boards would point you toward the "Stop the Bleeding" and "Communication Strategies" links to help you get started working out one on your own between the two of you (or three of you, if yoiu have a T) since from what I can see from my very limited start in learning DBT skills is that they can help but they're no one size fits all.
Before my partner's full breakdown, we had success working through the Stonewall most often when I offered radical space. Like, me taking a night or two away worked at first, but eventually only getting HIM entirely out of our shared environment worked. But then it ALWAYS seemed to, and sometimes something as small as an afternoon away (and generally involved in an activity) was enough.
Now At the time we thought he was dealing "only" with complicated Depression & Anxiety, so I apologize if talking about our actions like this might sound clinical or cold but since we figured it out by doing mood and behavior tracking I guess that's just how it sounds.
Anyway, I don't mean in any way to suggest that what (sorta) worked for my pwBPD will work for yours, but rather wanted to share that by working together you could find out what MIGHT.
Even before my pwBPD, his T, or I undeerstood he was BPD, he couldn't identify or express his own moods or needs properly, y'know? So I think that *for him* , the silent treatment was at least more a way for him to try and ask for what he didn't know how to express than a punishment for me, regardless of how I experienced it.
Whether you should give more space or press for interaction: IMHO that is an answer only the two of you can answer together, cuz every person and every couple is different. I've only been using them with my pwBPD for about a month but the advice in the "Stop the Bleeding" link and "Validation" thread in particular have been very helpful for me and my pwBPD compared to our previous interactions. I wish you both the best of luck and hope you'll keep us updated on how y'all are doing and feeling!