Go on a diet! No, seriously, here are some suggestions.

My experience is that you often can find food left in bear boxes that people give away. In the past, the ranger at Crabtree Meadow used to have a stash of food that she gave to people short on food. You could pack for 10 days and beg, borrow or steal two day's food! Most people take too much anyway so I think you would be OK. I have no pride - I have begged food off overloaded backpackers before!

Also check the location of all bear boxes. There should be a list on the internet. You may consider taking some of your non-perishable food into one of these on a separate trip before your JMT trip.

The other thing I have done (but it is not legal) is get the most important food in the cannister and counter-balance hang the remaining. Within a few days you should be able to fit all inside. Camp off the trail and a hidden spot - bears frequent the known sites and you are less likely to get cited for "improper" food storage if nobody sees you. What I left hanging was olive oil, sport drinks, coffee and tea, and other stuff that I could do without if it came to that and stuff that did not smell. There are smell-proof plastic bags too.

The ranger station at Kings Canyon (Cedar Grove) has some Bear-i-kades for rent - they may have an expedition size one. It is pricy because they charge more for the Bear-i-kades. These larger cannisters weigh the same as the BearVault.

I have in the past crammed 11 days food in a BearVault but I had to be extremely careful about bulk - for example all breakfasts of Malt-o-meal because it takes less room than oatmeal! Couscous is less bulky than pasta. Dried fruit and nuts is less bulky than trail bars.