There are specific areas within Sequoia/Kings Canyon NP boundaries that require bear canisters, but if you plan your camps outside of these areas, you can hike through them.
Here is a PDF map that shows the areas where canisters are required: http://www.nps.gov/seki/planyourvisit/upload/FoodStorageContainer_PageSize_20130906.pdf
We did this when we hiked the JMT and it worked out well. We only needed the “extra” space for a couple days and then were able to squeeze it in.
Of course, if I were to do it again I would probably hire a packing station to bring another resupply — probably over Kearsarge Pass.
Have a great hike!