After reading and reflecting a bit, here are some thoughts...

If I understand correctly, your post weighed PROs and CONs of two schools... the first, a public school, based on a recent meeting... the second, a private school, based on your son's experiences so far this school year.
- Has your son shadowed at the public school?
- Have you reviewed and printed your State laws and school policies for gifted education?
- Are you familiar with wrightslaw, a great source of information on disability?
- I'll just add the advocacy roundup here, too.

Public School
gifted pullout:
social - A great benefit of the gifted pull-out may be for a child to be in the company of academic/intellectual peers (or near as, depending upon the mix of kids which the school has to offer as peers). That said, a child would need to have the social skills to leverage this opportunity and make a connection with these academic/intellectual peers.
academic - What would he miss in the regular classroom at this time? Fun, challenging projects during two pull-outs of unspecified length each 6-day cycle sound like a very weak "gifted" program or service. Especially if only two topics are offered, and your child exhausted one of them years ago. You might wish to follow-up to see if you get a firm commitment from the school to expand offerings to include projects in chemical bonding/electron shells or genetics/heritability or something related to space.

As for differentiation in the classroom, you may wish to ask some gently probing questions as to what your son's experience would consist of.

Because the school only goes up to grade 5 and does not presently have an answer as to what math differentiation would consist of, you might want to follow-up on the school's response to your suggestions of Khan Academy and/or code.org, and get a firm commitment on logistics. Would attending the local middle school for math be up for discussion?

The OT consult of 30 minutes per week and social skills pullout with other children having similar needs appear to address 2e needs or deficits, not gifted/talented strengths. Do you also teach and reinforce social skills at home?

Private School
social - A child's happiness at school is an important factor. That said, does he understand that he will not be in class with his 2 buddies next year? When you say he is moving up to the next class and his 2 friends are not... do you mean he is skipping a grade... or his friends are repeating a grade?
academic - Although you mention that your son is happy at his school, you also mention that he reports that math and science are too easy.

Is it possible that in insisting on an aide for next year as a condition of your son's attendance, while also taking steps to preclude financial assistance by your insurance company, the school is establishing circumstances contrived to inspire your family to place your son elsewhere?

If the school refuses to budge on writing requirements, is this possibly indicative of a poor school fit?

In light of the discrepancy between your son's level 3/4 math placement and level 7 math enrichment pullout, you may wish to have further discussion with the school regarding the MAP score, your son's placement, and performance expectations.

School Fit
A small roundup of links on school fit:
- School consultant for elementary aged child
- What kids don't learn
- Roundup of Tamara Fisher blog posts
- Article about poor school fit (includes findings by Miraca Gross)
- roundup of links on "educational fit"
- roundup of discussion threads on full-grade acceleration (pro and con)
- advanced curriculum with same-aged intellectual peers

Applying for your child to join the Davidson Young Scholars (DYS) may be advantageous; If your son becomes a DYS you may be able to gain some additional advocacy support/information.

Lastly, be aware that with extensive data collection and the Longitudinal Student Database, schools may readily review your child's records from other schools.