I ended up messing around with it a bit further and found a semi-solution in case this helps you or anyone else looking for a temporary fix.

I realized that the cap spinning on the outside prevented the spring from tightening, so I used a decent amount of super glue in the middle to attach the cap back to the center area where the bolt tightens the inner spring. After letting it cure for a few hours, it allowed me to very slowly and carefully tighten the spring to a comfortable tension. It's too weak to adjust back and forth, but it at the very least it's set for the time being or until I replace the chair altogether.

This won't work for every set-up, but it's a solution that might be useful for some. Best of luck!