I've been having such great luck finding tons of JL J by using married segment and using CTS as the starting airport. As was mentioned above it even seems to nearly always set you up on the A350 to JFK.

I was wondering is there a particular city to use going from the US b/c CTS does nothing to open up more availability. I know to try Osaka, NGO, FUK, etc but just curious if anyone has found one that over time is best to get J or F to pop up how CTS does going the other way.