Thanks Electra and FaceBiter!
At my last job we dealt with issues similar to this all the time. Our RAP's were 6:30 am-3:00 pm. However, there was no part 117 so it was not uncommon to get a call from dispatch (also crew scheduling there) at 2:45 asking us to report at 16:00 for a 10+ hour duty day to cover delayed flying. In the summer we could get calls to report at 16:00 for 14 hours for overnight fire evacuations. They just didn't get the idea that we weren't sleeping around all day so that we could be rested for 14 hours of duty from the moment we were called. It got to be a pretty bloody fight, but the "fatigue" card works wonders!
Even if I wasn't capped at 16 hours, if you want me to fly until 3 am the answer is no! I was rested for 9 am and am reasonably functional as a human being, much less a pilot, until midnight, give or take. It's plain old common sense. You wouldn't ask anyone at CS to stay awake all day then drive their car somewhere throughout the night. Why would they expect you to do the same with an airplane! LOL