At long last, the mystery is solved!
The incredibly complicated layout of street numbers and addresses in Queens apparently does follow a pattern. This article has a great explanation. Unfortunately, even the simplest part is complex, as you can see in this excerpt:
The system works like this: Avenues run east and west and streets run north and south, the opposite of Manhattan's system. The avenues were given consecutive numbers, but often there were additional parallel streets in between the avenues that needed names, so they were assigned the same numbers and called roads or drives, in that order.