As you are all likely aware, there was an issue in the previous patches where items were not dropping consistently. With the help of Sky from Banana's development team and some other programmer friends I have now been able to find what went wrong and how to fix it.
Basically, my previous code was prompting the Steam servers to drop items, but not reliably waiting for that process to finish before moving on. So my code would prompt item drops, but only if that process happened very quickly. I have now switched to a different method that waits for the game to finish prompting Steam's inventory server, giving enough time for item drops to be prompted.
Thank you all for your patience, and special thanks to Sky from the Banana devteam for teaching me this process.