Between Oracle and Superior you have an opportunity for PIZZA and possible hitch to Kearny. I've heard that the pizza place there will deliver to the TH! That would be at the bridge between passages 15 and 16.
Superior to Pine - you will come out at Roosevelt Lake after passage 19 - possible hitch to Globe or Tonto Basin communities or a good place for someone to meet you there with a resupply box. Also, you come out at Sunflower after passage 21 which offers possible hitch to Payson or place for someone to meet you with resupply box here also. That I know of - neither of these locations have provisions to receive and hold a box but can't say for sure.
Pine to Flag - you will go through Mormon Lake which has an opportunity for lodging / food depending on when you arrive. I don't know if they accept and hold boxes but would be worth contacting them.
GC to end - you will come out within 3 miles of Jacob Lake. DEFINITELY stop for the baked goods!!!!!! Again, opportunity for lodging and food - restaurant and SMALL store with some resupply goodies. You may want to contact them about holding a box for you.
On the AZT web page, look under the tab "The Trail" for Gateway Communities. There's a map with links / info.
If you need boxes at Roosevelt or Sunflower, PM me and I may be able to help out.