In my experience the 'update.zip' method only works when you initially install the Rockbox bootloader. Once it's on there the stock firmware updating system will refuse to modify it, and will neither reinstall the bootloader code nor flash back to stock.
The only solution I found that works is to use the manual method outlined on xvortex' page. Unfortunately this means you need to setup a virtual machine running Windows XP, as Ingenic's USBBurnTool (even the latest 2014 version) still refuses to work on Windows 10.
As an aside, I found that the problems I'd reported here earlier were indeed caused by some corruption in the bootloader code. Rolling back to a previous version would work for some time, but then the boot-time panics would reappear. I eventually managed to dig out an old XP disc and spun up a VM for it. Manually flashing the rockbox bootloader again seems to have fixed everything, and I can now run the latest version without problems. This might be something to consider for those experiencing obscure crashes - if every other fix has failed, consider reflashing the bootloader, though it's annoying that you have to setup an entire VM just to perform one task.