Homeschooling has worked out very well for us. My son did early entrance to a private K for one year, but we have homeschooled ever since. In addition to food allergy issues, my son is 2E, which complicates his fit in a regular classroom even more than just giftedness does. Like your child, I'd put his LOG in the ballpark of Ruf level 4.
Speaking from experience here, the allergy issues are much easier to control at home without creating the sense of exclusion and "otherness" that might arise from being isolated during communal lunch time. There were a few terrifying instances during my son's Kindergarten year where other parents brought in food for the class without checking with the school first, and my son couldn't participate because they had made food that he was allergic to. Fortunately, even at 4 he knew better than to eat anything he didn't know was safe, and he asked about the ingredients.
As for the socializing aspect, most of that happens at lunch and recess. You get in trouble in school for socializing at other times! "Socialization", or learning how to behave in society, is just as easily taught in real multi-age interactive social situations as in artificially age-segregated classrooms where the only models for interaction are other children (who presumably also need to learn these things) and an adult who interacts primarily through giving direction and lecturing. There are plenty of opportunities to meet other kids and work in groups through clubs, scouting, civic and religious groups, homeschooling groups, and community-based classes, such as museum offerings or community theater.
You already know that he is unlikely to have a "typical" school experience, and homeschooling allows you to choose the level,pace, and mode of instruction that works optimally for your child, usually (depending on your state laws) without the need to clear it through any "higher ups". I would guess that, simply due to the nature of the bell curve, the bulk of the children in the gifted program are clustered near the cutoff score. You child scores significantly above that. It may be that a program that meets the needs of those learners well will still not be a good fit for your child. You are under no obligation to use it just because it is there. It may be great - I'm not trying to dissuade you from giving it a try - but I am trying to let you know that homeschooling may have more advantages and fewer drawbacks than you might think, and school might have more problems and fewer advantages than you currently seem to believe.
