Its the router that decides what to do with the connection. The HG612 acting as a modem acts on whatever the router is saying.
As you say the TR069 thing is what plagues a lot of BT devices, mainly the home hubs.
To the OP, I'd recommend you use a different compatable router. I use the ASUS RT-N66U. But I'm not sure of what connection your on, and others can recommend other routers too.
From what I can tell you've done everything right as far as the HG612 is concerned, as long as you turned off the settings recommended earlier in the thread. Imho you need a better router to replace the HH.
Demon => Freeserve => Pipex => Be => Sky => BT Infinity 2