"Is it reasonable to rely on the bear boxes in the beginning of the trip? Or is there a significant chance I can arrive at one and it's either no longer there or full? I found this map, which was updated as of 2009: http://sierrawild.gov/bears/food-storage-map"
It's hard to comment without knowing your planned route. However, if you are planning on dropping down into Kern Canyon from Mineral King, there are food storage lockers at Upper Funston Meadow, Kern Hot Springs, and Junction Meadow. If you continue up Kern Canyon to the Upper Kern Plateau, you won't really need a canister, as the bears are few and unaccustomed to human food-a PCT hang will suffice there. If you go up Wallace Creek via the HST to the JMT, there is a storage locker at the junction of the 2 trails. If you go south from there, there is a food locker at Crabtree Meadow where Whitney Creek crosses the PCT. If going north, there are lockers at Wright Creek and Tyndall Creek, as well as at the junction of the JMT and the Center Basin trail, and Vidette Meadows. I hope this helps.