I think Grand Canyon is a great idea and you'll go right by Petrified Forest and be very disappointed, but spend some time at the Canyon instead of moving on. Take a 3 day white water rafting trip down the Colorado. There are bus tours and mule rides down to the bottom, you can rent or bring bikes or take guided hikes. There is so much to see and do there other than take a look and move on.
And there is always the option of taking the car instead of the TT since time is limited and staying at Motel 6s along the way. Money you would save on gas would probably cover some of the cost of staying at the lodges. They are pricey but they have free shuttle buses to just about everywhere.
What ever you decide, you'll need to make reservations pretty soon so you won't miss out.