Hi, after talking on the IRC channel a bit I have reached the conclusion I likely have an RMA-worthy issue, but I believe I am required to post here for posterity and permanency. I'll answer the questions posed in the "stickied" post:
What revision is the board (e.g Revision A green / Revision B purple / Revision 2 purple)
Revision B, purple. Original shaped board.
What power supply were you using? (e.g. Smartphone charger, USB Adapter)
I have tried multiple supplies: a Motorola Nexus 6 phone charger, an Apple iPad charger, an Asus VivoTab TF810C charger, and a generic USB charger rated at 2 amps.
What is the ambient room temperature? (Rough estimate)
Approximately 68 degrees Fahrenheit (20 degrees centigrade).
What were you doing when it died?
Everything from just idling to compiling software and playing Quake. It seems to just be a matter of time and chance when it freezes, though compiling software or running 'apt' seems to make it happen more often.
Have you tried reflashing the NAND? Which image/OS?
I have reflashed the NAND multiple times, with multiple versions of Debian (currently using the 2015 Debian 8 release, but I have used Debian 7 in the past and hit the same issue), and one version of Android (Oreo).
Have you tried booting from SD card?
Yes, the Android Oreo image was booted from an SD card. It suffers the same issue, albeit less frequently.
Plus any more relevant information.
I don't know what else to say but that I kept assuming I was just running out of RAM or something until recently, when it froze with 'top' running and showing under 20% of the total RAM was being used.
It also happened once when copying a large file to a USB hard disk drive.