Im with Shred and the others, i've flown both with the boots in the bindings and out of the bindings, it basically made no difference. the bindings can handle a fair bit of abuse. Also if you are worried about the bag being too tall/thick etc. just take the boots out of the bindings and fold the back down flat to the board, no screws to remove or tools needed.
My suggestion is to just keep em on the board, fold the backs down and you should be good to go.