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. ???
I looked at a lot of 7up crates and other crates from ebay to try and put together a possible link to the numbers thinking the #6 could be for Cal. and other numbers for other states, but that didn't pan out. But I did notice that any of the southern Cal crates from 7up did have the #6. Even the shorter ones. I looked at other states but nothing correlated. So that theory might be shot down.
However, there could still be a connection between Sturdy Bilt cases and the Los Angeles 7up crates marked with a 6 - except that the Los Angeles cases were built earlier in Minneapolis and not in Jonesboro. ???