This probably ain't the best advice you wanted to hear, but with GCSEs sometimes you gotta neglect the subjects that drag you down. In the long run, GCSEs are just stepping stones to advance into A-Levels/College (etc..) - NOT something that will completely alter your life unless you completely fail or are looking to get into some prestige sixth form.
My sister was similar to you, her art GCSE was dragging her down in science since her teacher was quite needy about the artworks or whatever. So she kind of just.. stopped caring for it. Obviously did the bare minimum, but nothing more. She ended up passing fine, getting the A levels she actually wanted then.
Since you're now in Year 11 quite near to the GCSEs, I really doubt your HOY actually wants to let you drop the subject. Unless you have loud parents that will press the school, I don't see much changing there.
Also, there's not many benefits of extra GCSEs unless you really wanna stand out, for whatever reason. In the school I went to the teachers would actually REFUSE to give some extra choices, seeing it as impractical. You'll still get mostly the same opportunities as everyone else, honestly. I've never heard anyone caring for overall averages at all.