Nightmare, robbie! I have a friend whose son was just like this.
I think Batters has made a very good suggestion. Gradually introducing a slightly later bedtime would be my first thought, too, especially considering all the other tactics you have tried. After all, even half an hour's change would be great. 6.30 am is a whole lot better than 6.00 am.
However, and sorry, you won't like to hear this - my friend found that introducing a later bedtime had little or no effect on her son. The lack of sleep just made him cranky.
Your twins are just three - a difficult age I think, because they are going to grow out of day time naps soon.
Looking on the bright side, this could mean that in six months or so you will find they can go a whole day without flagging, but will be extra-tired at bedtime, and so sleep a little longer in the morning.
Will they be starting nursery soon? I remember my son went through a difficult sleeping patch at around three years as he grew out of day naps, but then he definitely slept longer once he had the rigours of a nursery day to contend with. Also, once your daughters attend nursery, they will be having a different day routine so this could be the ideal time to introduce a different sleep routine.
My friend never managed to get her son to sleep much later though. So what she began to do was let him go downstairs to play quietly or watch videos - making sure the place was very child friendly, of course. She used to creep downstairs with him, put a video on, and then go back to bed. He liked being taken out of his room and this seemed to stop him going back upstairs to visit his parents in bed. I remember being a bit shocked at this - her son was around four when she first started doing this - but she assured me her son soon learned to be quiet, happily occupying himself (mostly) and leaving her and her partner alone for another hour or so.
Lastly, my evenings tend to end late for similar reasons to yours. I try to practice some damage limitation: one early night (10.30 -ish) midweek to give me an extra burst of energy to tide me over till Friday.
Wish I could offer more constructive advice. Hope you get some here!