If you can get the involuntary commitment paperwork completed before he arrives, maybe they could serve him in the airport where he lands and transport him to Pittsburgh?
I'm sure it would be expensive, but doable?
Have you talked to the US Embassy to see if they could help you get the Denmark officials to bring him closer? I think that it would all be a lot easier if you don't have to cross state lines.
However, I think you're at the point where you need professional advice, probably from a lawyer, instead of asking on a forum. We're all going to be guessing at what you should do.
That doesn't mean we're not interested. I really would like to know what you're able to do in this situation.