Hi BrainDrab,
I ran the FixIt tool in Aggressive mode and then rebooted. After the reboot, a message saying something like "A script is causing your browser to run slowly. Do you want to stop running it?" Despite clicking "No" my system started to run very, very slowly - it took about half and hour to load everything properly. I tried rebooting again but this didn't help. I decided to leave it for a while and eventually things started to run normally again.
I ran a check for updates and the only one it found was KB3035583, which I hid. The "failed" update issue is still there - it attempted to download/install roughly 20 minutes after the initial check. The only difference is now nothing appears in the Update History despite it saying an update has failed. I assume it's the same Windows 10 one as before, but can't be sure since it no longer displays it in the History. There seems to be a lot of activity during and after the update attempts to install - computer usage goes up and the router lights flicker a lot more than usual even though it never successfully installs.