I don't know that a pro is a better choice, here.
Faye = Dose not want to talk. That she is going to talk could lead to a good place or backfire, spectacularly.
Marten is not pushing the issue, though. so that's good. His statements are objectively true. And he didn't lay on a guilt trip or a threat. There's a danger that "I'm not going to let you push me away," could escalate there, but here's the critical thing as to why I don't think this is job for a pro: Faye's choice not to escalate seems to be tied to the fact that Marten hit the spot. She probably has a lot of reasons to want to force an end to the evening, but she knows that she is pushing Marten away.
I'd argue the possibility that she was accepting that pushing him away was a consequence of her actions, but I don't think and unintended consequence would trigger tears, drunk-ish or not. Marten made her face up to the fact that part of her is trying to break up the team. That Marten isn't going to take that lying down probably creates a lot of emotional dissonance, given the fact that she doesn't like herself much right now, and has unresolved issues about how she has always treated Marten a little less well that he's treated her.
She needs pro help. No question. But this is a breakthrough moment, at least vis-a-vis her value to Marten or to herself.
Sometimes you have to seize the moment. It's not something I'd see as a solution, but it's an important first step that I don't think Faye is capable of taking with someone who isn't a friend. As much as Faye connects with the extended cast, the people she trusts implicitly are Marten and Dora, full stop. I really don't think Dora is an option, nor do I think she will easily reach the point where she's willing to admit that she's risking more than she wants to loose if the opportunity is passed up now.
Pro help is the best long term option, but I think there no chance of her seeking the best if she doesn't grab the lifeline Marten just threw her.