Just to update everyone: after this post, my Core went back to being nice a quiet for a while, but recently started clicking again and this time it was terminal.
I contacted Wahoo directly instead of just going back through CRC and they were fantastic — the sent out a new unit straight away and are only now worrying about collecting the faulty one.
The support guy said they would be sending me a 'tested unit' which is supposed to mitigate the problem. Interestingly, the shipping note and a sticker on the box described this new one as a 'Kickr Core
Platinum' which I can only assume is their internal code for 'we figured out the problem and these ones are fixed'.
Fingers crossed this solves it… only time will tell. This is what I get for buying a first-gen product!