You do need a bear canister for that last leg of the JMT. It's mandatory in the Whitney zone and down the back of the Rae Lakes loop, and you will meet a wilderness ranger several times along the way to make sure you have it - they are stationed at regular intervals at backcountry ranger stations and hike the trails checking things out. The Bearikade Weekender, which is lighter than the big BearVault, can be rented by mail and a skilled bear can packer with some repackaged meals can make 10 days fit in okay. I've gotten 5-6 days of food in a BearVault Solo.
I have a 40L pack that a Weekender fits in, along with my tarp, quilt, groundsheet, and the rest of my gear.
You don't say when you are going, but you will want to add a foam pad if you are going now. Regular low pressure troughs have been sending the night temps at elevation into the teens and the NeoAir isn't up to it all by itself. I've been comfy down into the 20s with mine, but it's just not made for low temps. The bag may or may not be adequate, depends on how many layers you have to supplement it.