I would wait until you are about 10 days out and can see the weather window for at least the beginning of the trip.
I would also rule out high elevation such as Flagstaff/Grand Canyon that early in the year.
Big Bend would likely have the warmest weather of the places you mentioned and some very nice back roads for your toad (we have driven most of them in a VW bus). And, some interesting things to see and do along the way, particularly from San Antonio west on U.S. 90.
And, depending on the weather, you can shoot south from home to reach better conditions.
And, at least for most, a 3000 mile week is enough!
