None of the suggestions helped, and I was about to perform a factory reset and reinstall when I found a YouTube video which seemed to place the blame on a bad battery. The comments called out bollocks, but since the my phone was marginally stable while plugged in to power, I figured it was worth a try – the alternative was shelling out at least £300 for a replacement phone.
Ordered a replacement Anker battery from Amazon, which arrived the next day. Put it in the phone, phone works perfectly. Yayy!