1st overnite, I think you are right, but corporate travel is really confused about this and I've heard of other cases where they refuse to book it.
However, if your entire duty day, from scheduled show, until the time your deviation deadhead schedules you to land at home (plus 30 min), is over 11+30 (without a full 8 hour rest period), you are entitled to book first class for duty day. If you tell them, "First class for duty day," they will book it and not give you a hard time.