OK, we cheated. We used a sleep expert but it worked. As it happened, we got lucky and the free phone consultation was all we needed to sort out DD1's early mornings.
I know it is different for everyone, but here's what we we did. The sleep expert asked if DD1 woke up ready to start the day or grumpy. We said ready to start the day and determined to start our's and DD2's day. She suggested we put DD1 back in her room, but open her curtains, give her some toys and tell her that she can start her day but mummy and daddy need more sleep and that she can come and get us when the sun appears on her gro-clock.
The first day she cried a bit and as the clock was set optimistically at 5:45, we had to return her to her room a few times. After a while we heard her playing and then she went silent for about 20 mins. This happened a couple of times, then we made a big fuss of her when she eventually came in and the sun was up.
The second day, the same thing happened but there was more silence and less playing.
The third day onwards she slept till her gro-clock changed and has done so ever since. We move it on by 5 mins every few days and are now at 6:50.
Oddly, the key to sleeping longer was getting her to start her day earlier. In the past we would sit downstairs in the dark with the TV on until about 7:30. She seemed to be using this as a substitute for sleep.
Also, the sleep expert told us we had to get the control back as she was controlling our mornings. I don't really understand how this worked but it did and I wanted to share it in case it works for anyone else.
If not, please don't be embarrassed to use a sleep expert. They are not cheap, but you might get lucky.