Need a chair for a heavy but short person - 10+ hours at a time?

Recently accepted a new WFH position. I am also a gamer. So i'll be working all day on the computer, and hopefully able to play games a bit too after work is over. Right now i sort of dread being sat for too long, or i dread standing up after sitting. Whenever I sit at my PC for more than an hour, I've been having Sacroiliac (SI) joint pain. It's alot of pain on both sides of my tailbone almost, like my "sit bones". I've talked to my doctor about it and I got a cushion lab cushion, and i've tried a purple gel cusion, neither are doing much. Both are better than without though, for sure.

So i am looking for a new computer chair. I've look extensively at gaming chairs and ergonomic office chairs. The problem with being big but also quite short is that most chairs built for a heavy person are also quite tall. I already sit with my feet on a stool because my current chair is a bit tall. I have short legs lol. Would love something under 500 dollars. Bonus if the arms go up and down.

Any good or similar experiences with chairs that would suit me?

5'1'' 300lbs