So, while trying to disassemble the throttle shaft, I snapped one of the bolts which gave me an idea. I had this second carb that came with the car as a spare part when I bought it, and I've been pulling parts from it onto the other. I never tried testing it but I put it on and it works like a charm! It's a DMTRA and I have no way of controlling the choke from inside the car, but still, the car runs! I probably should have done that from the beginning.
The shaft was very loose on the DATRA and I'm pretty sure that was the problem. The DMTRA's shaft was firm and works great.
But thanks for the help anyways, guys!
My next project is figuring out how to move around those coolant hoses from the water choke from the last carb.
Side note: What does the number on the stamping of the carb mean? One of them was 32 DATRA 100 and the other was 32 DMTRA 200, I am referring to the 100 and 200.