Had another senior advisor contact me today and went through a whole bunch of testing, took the better part of an hour. He had me change notifications settings and when he started sending me test emails, they came in while screen was locked but not when it was unlocked. He was convinced it was a notification issue.
I pressed him that I don't think it is as the behaviour over the past couple of weeks suggests otherwise. He then sent me more test emails, some came in instantly while others didn't, whether the screen was locked or not, so he deemed it "intermittent".
He had me forward a few screen shots of my settings and said he's going to forward all the notes to engineering. He suspects what might happen next is they could install a profile on my phone and run it for a couple of days then generate a diagnostics report. The battle continues.