If I’m remembering correctly, I’d expect more of a hard close than anything else at the end. They want you out.

I can’t remember if that meant things like the Emporium and the MSB were still open as we were walking out, or not? Hopefully someone with a better memory than me knows for sure.
As for the lanyards, yes, they have historically started distributing them at/around 4pm... if you enter the park before then (which just for full clarity would be using another park admission type, not your DAH ticket), you’d need to go back “up front” at some point to get the lanyard. It’s not like
MNSSHP and
MVMCP where they set up check-in/wristband stations at places within the park.
Hope that helps!