The bike is running today! I was able to take it down the street a bit. The carb was very dirty, and still needs to be cleaned a bit more. The idle air screw was pretty dirty, bad enough were it was bottomed out! Had to reset it to 1 3/4 turns back from the get go. The valves need some adjustment, but all in all it seems to work!
The gear I ended up getting was still a bit loose, so I put an extra shim in there, and it kicks over much better. I'll have to look into getting a new gear, though. I'm worried that extra shim may cause the shaft to break.