I wanted to figure out a way to fix it. After all, it's not like I need the mechanism to work properly. I want it to stay all the way up, all the time. It doesn't need to move up and down to keep me happy. So what if I could just prop it up somehow? And that's when I realized, someone has probably thought of this already. And that's correct.
I think my search term was "office chair repair." If you search that, you'll see results for replacing and repairing the gas cylinder, but as I mentioned, that's more of a fix than I was looking for. But right there alongside that suggestion in the sponsored results, something caught my eye.
It's kind of like bracelets for your chair. Big thick bracelets you can slip on. Exactly what I was looking for. Less than $23 total and it took me less than a minute to slip them on. They left a gap of less than half an inch, perfectly acceptable.
Always google it, somebody probably already made the thing you need.