During my lunch block, I was able to fix the gear skipping problem. I added Lego pieces on the other side of the gear, forcing it in place. It was then able to life the 200 grams no problem! Here is a video of it (sorry for the vertical video):
When we got to class the next day, we started to work on actually completing the challenge. But we ran into a problem: the weight made it too heavy to turn. So I changed the gear ration of the turning setup so that there was more torque. It still has trouble turning counter-clockwise, but clockwise is fine, so Ethan made some code for it to raise the weight, then turn and drop it. You can see that here:
At the end of next class will be our first trial. All we need to do is fix that turning issue and we will be ready!