I'm interested in this question, but have reached very few conclusions, other than obvious ones. When I was feeling joint pain, but before I was diagnosed, I made an effort to cut out / down certain foods, such as butter, cream, processed meat, sugar etc. I wasn't overweight (not seriously anyway) but I thought losing even 1-2 kg would at least not do any harm.
Since diagnosis and being put on methotrexate, I've also pretty much ditched alcohol and try to eat foods that supply folic acid (in addition to taking prescribed supplements). I also keep a diary with the idea of monitoring food, exercise, movement and pain levels. This is a useful thing to do for all sorts of reasons, but it hasn't helped me see any correlation between certain foods and pain levels.
I did read that 'nightshade' vegetables like aubergines (egg-plant), peppers or even tomatoes could trigger inflammation, but they don't seem to affect me one way or the other. Which is good, as I love aubergines especially.
I really don't think I'd want to do one of those diets where you cut everything with potential to cause inflammation then try to build things back in one by one ; at present there doesn't seem to be a compelling reason to go that way.
So yes, agree with most of what's been said already.