In case anyone else has the same problem, I contacted NI and they got me running again by pulling TraktorSettings.tsi out of Documents/Native Instruments/Traktor###(latest version) onto the desktop and running the install wizard to reinstall the X1.
I had already tried pulling all the X1’s install files out to achieve a similar result, to no avail. This worked, but I did have to go through Traktor’s notorious Settings menu all over again (and reinstall my S4 as well) – but hey, at least it works again.
And kudos to NI for a prompt and helpful response.