It seems like the papers are almost a formality at this point ... ?
You had an episode where you tried to get her to leave, then you offered to leave and proposed that the two of you would take turns leaving the home (presumably for the sake of the 16 year old?), and she cycled through a few attempts to change your mind, ultimately landing on "good behavior" before (I assume) she regressed back to default.
So it's likely she knows the papers are coming?
Is this more about how to handle her stonewalling and obstruction more than how to deliver her the papers?
There's a good chance she wasn't serious about getting a divorce but the nature of having BPD means, well, you know what it means.
I have two ideas for a next step but not sure how to proceed
BPD can cause behaviors that are challenging, but for the most part the ones that get hairy when divorce is in play include: domestic violence, false allegations, self-harm, suicidal ideation, parental alienation, substance abuse, draining bank accounts/over spending, infidelity, smear campaigns. The most common one that comes up here seems to be stonewalling and obstruction.
What type of response/s do you anticipate from your wife?
I would start with that knowledge and then plan the discussion around what you anticipate.
The discussion is the catalyst for the other things you anticipate will happen next. Look for all the junctures where you need her participation and then assume she will stonewall. Then have a plan for handling that.
You have expert knowledge on how she behaves in general, so then it's about having the next 5 or 10 steps in place for when she gets there. It helps to know what she cares about and then look at that as leverage to motivate her to comply.
Being 5 or 10 steps ahead is key to reigning in the worst of a high-conflict divorce. Some things cannot be avoided so the best we can do is make things less awful.
Maybe we can help you think through what is most likely to happen and how to set things up so that her responses are just part of what's expected. Chances are, you have some kind of leverage, or can create some kind of leverage, so that she is presented with choices each step of the way, rather than always choosing "no, nope, never."