Personally speaking I would stick to Grand canyon and Zion NP as you have seen neither before. With a day and a half of travel it only really leaves you a day and a half at each to explore with a little time to enjoy the journey in between. As Buck mentioned, a trip on Route 66 through Kingman, Peach Springs and Seligman. That will still allow you some time to enjoy the Grand canyon that afternoon and the following day where you could stay in the park or exit via the east entrance and stay at Cameron Trading post to give you a 'head start' the following day. On route to Zion you could stop at Horseshoe bend, Marble canyon and Checkaboard Mesa to take in the views. Just before the Mt Carmel tunnel into Zion there is a small parking lot for the Canyon overlook trail. Unless you stay in the park, Springdale has a variety of lodgings and is a lovely little town. If Antelope canyon is a priority then you could make it work and you certainly could visit some of the great suggestions made by Buck, it's finding a balance between quantity and quality that suits your idea of a good trip.