They freaked out when I told them I didn't want to complete the interview loop because apparently I had passed their initial "weeder" interview and they were getting really excited about the possibility of me joining. But I would have had to sign that "everything, forever" NDA to keep going, and they weren't willing to go back to legal or do anything to change it, so that was that.
I personally know several people in my state who had their careers impacted due to threats from former employers over an NDA, so I really don't feel like that was an overreaction on my end. And I'm super-happy where I ended up.
I just wanted to provide a data point on how NDAs that go overboard ("everything, forever") can cut both ways.