I generally only ask to be “made whole” and have never requested additional “compensation.” I doubt AA would pay my hourly rate in any case. There have been times when AA has thrown a few miles my way in an effort to be proactive, which I genuinely appreciate. I’d say your situation is a 5-15k miles type event.
I share your frustration with the AA trick of blaming a totally obvious mechanical delay on “weather” if there is light rain anywhere in North America.