My advice is to not overthink it - I am sure that the private school has had other less-than-stellar recommendation letters and I'm also guessing that even though they won't advocate for a skip, the principal and teacher might pull through with a very nice letter of recommendation.
Are you worried that the letters will work against your ds getting into the school or just worried about them working against acceleration? Or does the school start at 6th so he won't be able to get in if he's not accelerated? If it has a 5th grade, I'd second Grinity's advice. I'd also add that, we have our ds12 and ds7 both in private schools (two different schools) that say they work ahead of grade level and have a high percentage of G&T students - and they really do! Sometimes it's just an ad with nothing behind it, but sometimes it's true.
Good luck!
polarbear