I realised that while a couple of bits of software (WinTV, GBPVR) apparently gave a perfect picture but the others didn't (MCE, MP), they failed just like the rest when I tried to use both tuners at once. From that I suspect that this is a hardware/signal issue after all, since it would appear that my Hauppauge tuner can't handle the low quality signal off mux 2 but my BT Vision box can.
So I'm either going to have to invest in another tuner - don't like the idea of buying expensive tuners at random and hoping they'll work though. Or getting a professional to have a look at our aerial setup - more expense but hopefully a good chance of a result, we're only 7 miles from the transmitter!