I too have ordered the Japanese meal in F on LAX-NRT-SIN and back.
I've always asked for caviar and the western dessert with no problem.
They usually even go to the trouble of setting the table with everything for the western meal and then remove it before presenting the tray with the Japanese meal.
The only times I've ever had an issue with them having to wait and see what is available is if I order the caviar and then ask for the other starter as my main course.