Alright everyone, the issue has been solved and it was a very simple one at that. The carb tuning instructions that my weber came with skipped a step. I looked up some generic carb instructions for a different weber model and compared them to mine. Evidently before starting the vehicle the first time I needed to hold the butterfly completely open with my fingers and then rotate the linkage fully. This set everything in place. Now the linkage touches the set screws that its supposed to. After some slight tuning, the Brat idles normally. Now I just need to put the air filter back on, reconnect the accelerator cable, and take it for a drive.
I will be adding a throttle return spring for the added benefit based on your feedback though. Thanks!