Carl,
You could back up your films to an external Hard Drive. See:
http://hummy.tv/forum/threads/things-every-hd-fox-t2-hdr-fox-t2-owner-should-know.1858/#post-28600
Then you could reformat the hard drive, carry out a reset and manually tune to your best MUXs. This will put the box in the best state for any further tests, if anyone can come up with any.
Without loading the Customised Firmware you are limited to what you can do with the Hard Drive.
The signal level and quality figures you are giving seem to indicate all is well but, obviously it is not.
One further test you can do, and avoiding the BBC channels, is to try recording ITV1 and watching ITV2 - same MUX so you should not have any problems, as far as I know. Then switch to watch ITV3 which is on a different MUX and that should cause the problem to appear as a new tuner is required.
Sorry you have to do all these tests but your problem is challenging.
Martin