Many thanks. I cleaned the clock board as described, which seems to have fixed the clock problem completely (BTW it is not necessary to remove the hard drive to get at the board if it is not being replaced, just cleaned). Who would have thought that cleaning an area of PCB that looked perfectly clean to start with could have such a beneficial effect?
No change in the recording problem until I manually retuned to exclude channels not from our local transmitter, as advised by Humax Support.
All good as new now. Deeply grateful to the experts involved.