So I contacted Motorola via live chat, only to be told to call tier 2 support. Not wanting to actually talk to a person, I persevered. I'm pretty sure the phone was still on but may have been off for a while (can't remember if I force powered it off or it was stuck at the blank screen after booting, but this may be key in fixing it). I then press and held the power button (turning it on or force rebooting), and didn't let it go, holding it throughout the boot animation. After doing so, the "Upgrading android" screen appeared and I breathed a sigh of relief.
So there you go: what I did to fix it, and what you can try if the same problem happens to you.