How is his writing? What are the writing standards of first grade versus K? Social maturity?

I agree with PPs about the possibility of testing giving you more information. My boy is a couple months younger than yours and going into the K equivalent at a private school (UK curric). He's crazy advanced at the school, but they have exceeded my expectations and done well meeting his needs. We're leaving him at grade level at the moment, but the school has agreed to out-of-level testing -- which we can use later if needed to support a skip.

In your case, knowing the school isn't supportive of advanced kids, it makes more sense to look for a skip now. I'd still want to know what the writing expectations are in grade 1, and social aspects wouold be a major consideration.

FWIW, I've read that first grade is the grade to skip if possible, as the day turns from more play to more sitting-down school. That's a major reason we haven't pursued a skip; our boy would rather play all day.