I would say; log the time the way the FAA wants it to be logged and then adjust the times on the application for the way the employer wants. I wouldn't refrain from logging rotorcraft time as part of my total time because Southwest does not count it towards their total time, I would simply subtract rotorcraft time on the application. I highly doubt that anyone would show you the door because of this, you are putting less time than the time you legally have.

Companies specify what they want when they ask for times because you can and are suppose to log time the way the FAA says to.