I've been lurking on this thread for a while and finally have something constructive to add to it.
I got the invite to take the online assessment at the end of May and took it about a week later (due to being out on a trip). Sent in my NHPS form, but didn't get an auto-response like we do when we update our resume & PAQ. So I called HR today to make sure that my NHPS form was received. (It was, there's no auto-response set up on that inbox.)
Here's the latest from HR: Interviews currently scheduled for the end of June (as previously noted in the thread), but that may get slipped. There's about 15 folks in line for a phone screening right now, but there won't be any phone screenings done for the next week and a half due to other things going on within HR. June & July classes scheduled, but she doesn't know beyond that.
She said I'm in the queue for a phone screening, and we even talked about one of my "issues" (a recent training bust.) She did let me know that in a case like mine with a training bust, they'd cover that in the phone screen, and then take it to one of the management pilots (I didn't catch who she said it goes to - training, CP, standards?). It's not a kiss of death to have one, as long as your attitude about it is right (accept responsibility, know what you learned from it), and the rest of your resume / record is what they're looking for.
Hope this helps others like me that are just waiting on a call.