Illinois Glass merged with Owens Glass in 1929 to become Owens-Illinois. But its still a good clue. The thing is, we really don't know who made the 3-1-3 number 6 Los Angeles crates. Just because they got their bottles from Owens-Illinois doesn't necessarily mean they got their crates from them as well. Its even possible there was a surplus of Illinois Glass crates that were used after the 1929 merger.
Another thing we don't know is if the locations were stamped on the crates by the bottler or the crate manufacture. Its possible they were blank when shipped and the bottler stamped the location on them. ???