Thank you again, I tried this earlier and it's all it was, thankfully, it all works now.
We had found a strange metal clip-like piece early in the season(clearly was not even from the tractor) which led me to figure out that the choke wasn't responding to the movement of the throttle, and we kind of let it just sit since I'm not very well versed in engines.
But I tightened the cable, and now choking the engine on the throttle closes the valve properly.
Thanks again, I really appreciate your time. You saved me a bunch of time and money.