I don't have any links to sources, but have you looked at PotentialPlus? They may have relevant data.
Is your child in a UK state school? I don't believe the curriculum is all that good at providing for exceptional children: the Gifted and Talented scheme stopped some years ago, and the 'mastery' approach encourages breadth rather than going ahead. Moving up a year is extremely rare, and can be problematic socially, and in any case wouldn't make much difference for a really exceptional child.
We found each teacher varied in their approach in primary. Some teachers were happy to extend and clearly enjoyed teaching an outlier, but in other years our DD just had to make the best of it. We encouraged her to finish her work quickly (but accurately) and to ask politely for something harder, which sometimes worked. She always had a book in her bag, and sometimes a puzzle workbook for those times when she'd finished everything but the teacher was busy with other children.
For our DD, primary school was a happy place, with some learning and plenty of good social development. We didn't expect too much from the school - we decided early on not to push unless DD was unhappy - and it was fine. She still passed the 11 plus easily without external tutoring and is now happy in her chosen grammar.
Extra-curricular activities stretched her in different ways. Most waking hours are not spent at school!
Our DD probably isn't as exceptional as yours though. She never became disruptive or disengaged in primary, but whether that's because she's not exceptionally bright or is just very compliant, I can't be sure.