Hi jaffa
Have put my teacher hat on for this. Here's my suggestion as to why this might be happening with your little boy (who sounds fantastic by the way!)
Carpet and circle time are different to being "on task" at a table. Just like us adults, sitting listening to a presentation, its a time when your mind can wander, particularly if you are tired (cos you're a bright little button who is up at 5.30am!). Also because he's clearly a bright spark, some carpet and circle time might be just plain dull and therefore he will switch off.
School being what it is today in Y1 (hard going and tiring with a very focused numeracy and literacy hour every day) he probably does need to get more sleep as its only 10 hours which may not be giving him the brain fuel to get through the day. Easy for me to say, and I don't have experience of getting 6 yr old to sleep. I'd say goodbye to the little loves at 3.30 and my two are 2 and 9 months! One thought though - do you have blackout curtains for his room; if its the lighter mornings waking him earlier, this might help.
With regard to what's happening in the classroom, firstly, don't worry too much about it - carpet fidgeting and losing a bit of concentration is pretty common in in Y1 - they are only little and we expect a lot from them!
It's important that the teacher doesn't make a big thing out of it (I'm sure they aren't at this stage) as this can make a child switch off more.
If it was me, I would be making sure he is getting plenty of questions directed at him (and his ability level) to keep him engaged in whatever is going on in carpet/circle time.
Talk to the teacher about his change in sleep pattern and perhaps suggest he sits fairly near her/him on the carpet so eye contact is easier to keep. Also ask if he's answering many questions and this should prompt the teacher to direct more questions towards him if this isn't already happening.