So I assume he's ~13yo? What's his size compared to the Pee Wees? I would hope the coaching staff for both levels can appeal to the rec/house league for an exception to be made? A compromise may be to do half-season with pee-wee (which I assume remains no checking) then jump up to bantam (which I assume still allows checking)?
He's not going to have a good developmental experience playing that far above his skill level. And the house league association is likely going to lose him (and future situations like his) as boys will decide to sit out, or parents will remove their kids. Loss of participants and $ to the league / house.
I've posted before I didn't play organized hockey, but many of my friends, classmates, and/or friends siblings did, even through Junior, College, 1 went to Sweden for pro, etc. But, I am familiar with the age/skill thing. I skipped a grade, and was therefore smaller and less experienced / skilled in any/all sports until I grew to average size ~sophomore year (turned 15 midway through that year).