Thanks for this thorough analysis!
I agree with everything you stated, and have the same findings, however there's one issue where I have my doubts and that's the first one you mentioned: Food!
Food must have at least some influence as many people on fora report improvement restricting gluten and increasing food that contains magnesium.
You say there's no scientific evidence for the influence of food, however since food affects the quality of the bacteria in your gut, there is an indirect evidence that food surely matters.
Take for example the Chinese boy from the link below where researchers transplanted poo bacteria from a healthier other person's gut in his gut, after which the amount and severeness of the tics decreased significantly.
https://www.google.com/amp/s/www.dailymail.co.uk/health/article-5307749/amp/Boy-9-tics-cured-POO-TRANSPLANT.html
A promising method, for more issues than tics alone. We may try home made Kefir to improve the quality and composition of the gut bacteria.