I bought this a few years ago and have been pretty happy with it: [https://www.amazon.com/dp/B00IKBL2ZS/ref=cm_sw_r_cp_apa_i_3rT6CbHY8H8QF].
It's over your budget, but as others have stated, it's risky to go cheap on a work chair you plan to use for hours at a time.
Another option if you're not looking specifically for an office style desk chair might be an upholstered Parsons dining chair or similar. They're nice and cushy, and you can find fairly basic ones at reasonable prices on Amazon, Wayfair, and sometimes at thrift and second hand stores.
I'm 6 foot tall and a little over 300lb, this is the chair I bought 6 months ago. LINK
I spend most of the day and evening at my desk (ref 300+ lb!) The back of the chair being open mesh is nice and cool. The gas strut is rated for way more weight than I am. I'm not sure if it's available in the US as I got it from Amazon UK.
Can confirm I am sitting in that chair right now. Don't know where you are but here is the amazon uk link:
I don't care for swivel chairs and I have recently purchased this, similar height and weight to your self.
Available from amazon
Oh gotcha! Well the chair idea I guess you could squirm a bit, but you might end up on the ground of you do too much haha. Maybe you tie the waist to the back of the chair?
This is the chair I use. It has padded arms and are a good distance apart. Im 5'6" and its not too uncomfortable to sit with my legs spread on the arms - ive sat there for 30-45 mins before. The only thing that gets tricky is they get a little slippery when you start to sweat. Covering the leather arms in a fabric might be good if you bind their arms where they cant prop themself up.
Deal link: Amazon
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I like the last one for looks, but I'd probably go for this one personally as the early ones look too close to the same cheapy office chairs that I go through.
I've bought a couple of these in the past, they have never cost the £312 they claim to be worth but its a pretty decent chair for £99.
Drum thrones make awesome guitar stools. It costs a bit for a quality one, but your ass will thank you. Alternatively, look around for office chairs without arms. This is what I have in my room and I love it. The leather feels very high quality, for the price, and it's been very sturdy so far.
I bought one of these a few months back and it's real nice. I spend all day and most of the evening sat in it and it's comfortable.
Also, this is one option I found on Amazon for a possible office chair, but it's only really made for big people, not tall people too. Plus, the legs extend all the way up the sides of the seat which if my feet are planted on the ground, my knees are in an outward position which would probably cause discomfort if it digs into my legs.
Boss White Leather armless I also have a chair pad I've used for years as well that I put on top of it. It's comfortable to me.
Although the chairs in my college library are stupid comfortable but they cost $400 a piece. I might end up buying one some day.
This is what I have
Had it for a little over a year now, still as comfy as it was on day one.
Thanks to the mesh back, don't get horrifically sweaty in the summer, and it means there's no internal padding to shift and move about as you use it.