(((hugs))) you must be exhausted.
We had great results with the Groclock. We used it in conjunction with a gate at the bedroom door so that my DS could not just walk out of the room (else he would have, for sure). The clock will only work if you are 100% consistent with it. We told my son that if he looks at the clock and sees the moon, that means mummy and daddy are sleeping and his job is to grab his lovey, stretch, roll over and go back to sleep (we role-played this so he knew what was required of him). He was waking pre 5am so we set the clock for maybe 5.30 to begin with. Of course, the first morning there was a huge amount of screaming at the gate he had a major tantrum that things were changing up on him (we expect this from toddlers, right?). I stayed in my room and any time he quieted down a little I would say "The moon is on your clock. Mummy is sleeping. It's sleep time."
As soon as it hit 5.30 (he had screamed the whole time), I went into his room, turned on the lights, gave cuddles, showed him the sun on the clock and reiterated that now it's morning time we can go downstairs.
The second morning he screamed for a while but did eventually quiet down.
The third morning he screamed for a while but did get back in his bed. After that, I started moving the clock forward by 10 mins every couple of nights so very soon we were at 7am which was our wake up time. He would wake up, briefly look at his clock, and go back to sleep (just as you or I would if we woke up at 4am).
With such short nights, I would doubt your twins are under-tired, I would suspect more that they are already overtired. If you can't get them to bed earlier then I hope the Groclock will help them get some more sleep in the morning.
I hope that helps. I would strongly consider a gate at their door, else I don't know how you will get them to stay in, unless you are prepared to do a lot of silent return with them - I couldn't do that with my son it was too upsetting for both of us he would go hysterical.
