Update for anyone who's still remotely interested...
Final analysis when 2nd BT engineer came this morning:
Lots of problems, error correction etc. on our connection. He's swapped the pair from that line with the other pair to our second line (which has bog-standard ADSL on it) and the problems his kit was recording have gone.
We're just waiting now for the line profile etc. to be reset and hopefully that'll sort us out.
On the plus side, BT now admit it's a fault and it's off our premises, so if it doesn't resolve now, shouldn't be hard to pass it back to them. Yay. And we've now got a new modem, new modem PSU, new VDSL faceplate (as it was the wrong one) and a spare router cos we bought one last week just in case...
And a big HOORAY for Leo at Zen, who took this on board and got things rolling. Thank you!