Welcome, nmc3586!

Originally Posted by nmc3586
What would you do???
You've received great replies already. I'll just add a few thoughts. I would begin by read up on choosing a school, school fit, and advocacy.
Some posts to consider:
- Roundup on Advocacy (includes working with schools, meeting prep, school fit)
- Article about poor school fit
- What Should Everyone Know about Gifted Education? This thread includes discussion of gifted "myths."

Originally Posted by nmc3586
what is best for profoundly gifted kids?
What is best for pupils is having their educational needs met. All children need appropriately challenging curriculum and intellectual peers. Typical children may have these needs met in a typical classroom with a typical mix of children. For gifted children, special planning and effort may be required to provide appropriately challenging curriculum and intellectual peers. That said, the profoundly gifted are not a monolith. Even the same IQ score can look different on different children, as each may have their own unique combination of strengths and relative weaknesses. For each child, validation and affirmation may be found in different circumstances.

You do not provide background on your child's elementary school experiences and learning environments, which may be helpful for making decisions for middle school.

Your post appears to contain a number of artificially limiting statements/assumptions or pairings of ideas, which may not serve you well in managing expectations, but may instead obfuscate the identification of the least-worst option. Like gifted myths, they may negatively impact the ability to make a successful placement, and evaluate the fit.

homeschool
- "would miss the social aspect of school too much"
Many homeschool students are very social and gregarious and enjoy the company of neighborhood friends, and those in special interest and activity groups in the community, such as participation in art/music, as well as above-level math summer camps, etc.

local school district
- "severely underfunded so pretty poor quality"
Correlation does not imply causation, other factors are often at play. For example, read about Jay Mathews and his discovery of high-performing pupils at disadvantaged James A. Garfield High School in East Los Angeles, where 85% of families had incomes low enough to qualify for federal lunch subsidies... yet the school produced 27 percent of all Mexican-American students in the country who had passed the three-hour-plus AP Calculus AB exam.
- "few electives if any"
Although there may be few electives, if art/music are offered, this may be a match, and your child may find company among pupils who share those interests.
- you do not mention whether there is any gifted support, cluster grouping by readiness and ability, acceleration, etc.

"best" public school in the state
- "pay tuition to attend"
I am not familiar with the concept of paying to attend a public taxpayer-funded government school. Would you explain a bit, to help me understand?
- "we don’t live in district so he wouldn’t have friends nearby"
If your child has friends nearby now, those friendships may be expected to continue. There is a difference between friends and classmates. While there may be a 1/2-hour commute to this school, there may be other pupils from your neighborhood attending this school. Additionally, for any pupils who live within the district, classmates who form friendships may live at opposite ends of the attendance area and may therefore be a similar distance apart (1/2-hour).
- "rich and white, and we wouldn’t necessarily fit in (or want to embrace that culture)"
Rich and white is not a culture, rather wealth and skin color are two demographic labels. One can easily "fit in" with those having similar interests and pursuits, regardless of demographics.

public magnet/lottery school
- "the curriculum is not accelerated or advanced"
This option may require extensive homeschooling outside of the school day. Additionally, if attendance is by lottery, one needs to have a backup plan in place as there would be a possibility of not winning the attendance lottery.

low-cost private school
- "rigid founder-led administration that is not open to parent feedback" appears to not mesh with "lots of advocacy"
- "Acceleration might be possible"
One would typically want to know the acceleration policy proactively, before enrolling. This would include knowing the test instruments, cut scores, and proposed placement for one's pupil.

Originally Posted by nmc3586
What would you do???
Having considered each of these points, I would have a family discussion, including all stakeholders in identifying the least-worst option. If your child helps in evaluating the PROs and CONs of each option and contributes toward decision-making, he will be more likely to make the best of the learning environment he has helped to choose.