I go to a grammar school also, and whilst I am SUPER sick of the atmosphere and people, I don't think I'll move (I'll have to make a decision soon though).
I want to get very good a level grades, and I think I stand a better chance at that if I go to a grammar school because they push you.
I would only move sixth form if I got some amazing scholarship into a really good private school (which is never going to happen lol)
I live 45 minutes away from my school by public transport (when I get dropped off by the bus stop), but if I was to go all the way to school myself, it would take well over an hour. I know where you're coming from, when I'm travelling to school, people from my local school haven't even woken up yet, so if you really don't want to wake up early for more years, maybe consider going to the sixth form college.
I basically don't want to move because I don't want to start again somewhere new, with no one I know. I'm not really used to state schools as I haven't been to one for 4 years, so it may be a big change but idk. Plus, I go to an all girls school so my conversational skills with males aren't exactly polished (they're non existent lol). But, even if you don't want to start afresh at the sixth form college, if you do it will be a good experience, and I'm sure you'll make friends.
I don't know, I'm sick of my school and the people especially but I think I might just suck it up. However, you're in a different situation to mine because my school's sixth form has all the options I want to take whereas yours doesn't. What do you want to take at uni? Does it involve sociology?
Ultimately it's down to if you really think it's worth it to move or not.
This rant probably didn't help you at all lol. Anyhow, good luck with making a decision