My wife and I did the Southern Tier last fall. She supported me with our van, so it was a very similar experience to your plan. We found that our daily plan was heavily influenced by our choice of where to spend the night. We were tenting when we could, and using motels otherwise. I was hoping to avoid putting the bike in the van again until reaching St Augustine, but two mechanical problems, and concern about our schedule changed that. As a result, there were several times that I started out on the side of the road where I had loaded the bike the night before. If you decided to do that every day, it would make your choices of overnights much more flexible. Also, you could avoid many of the less appealing locations and situations.
I did a blog as I went: http://wendell-tripfall2010.blogspot.com/
We decided at the beginning to take a rest day every 4-6 days. Most of the time, we did things like laundry on our rest day. But we also visited the Blythe Intaglios, a museum in Tempe, Gila Cliff Dwellings, McDonald Observatory...
Four dogs will keep you busy!
There are lots of campgrounds in the southern states that cater to the Snowbird people. In Oct-Nov-early-Dec, the Snowbirds hadn't arrived yet, and there were lots of campsites. In March, they may have left for home, but I don't know. But, the campgrounds were sometimes full on Fridays and Saturdays, especially near large cities.
Enjoy your trip!