simple: if you do a VVR resupply as your final southbound resupply, you just have to kick up the pace. 20 miles a day should do, and you'll get there just fine with just one full bear can per person, assuming you're not just packing rice cakes and marshmallows, but really dense food.
If you don't exit at Kearsarge to resupply in Independence, or have packers meet you at Charlotte Lake ($$$), for a more leisurely JMT there's really no way around the Muir Trail Ranch. An easy 8 days from there to exit, and it'll fit in any can.
Now there's a small detail that the guidebook you have may not have mentioned and it is what a lot of people plan to do when resupplying at VVR: It is legal to hang food between VVR and Pinchot Pass. So, if you a) can actually carry all that food, and b) know exactly how to safely counter balance hang your food that doesn't fit into the cans, and camp every night you have food that doesn't fit near a tree that actually allows safe hanging (good luck), then you could technically pack 14 days of food at VVR and slowly drag yourself down to Whitney, always looking for a good tree to camp at.
Another option is to mail food to Parcher's Resort and after the VVR resupply exit again from the MTR at the Le Conte Canyon Ranger station and head over Bishop Pass to Parchers shower and resupply there, then and go back in. Much closer to the end of the trail than VVR, even with the detour. If you are somewhat adventurous, you can also shortcut to the MTR at Palisade Lake from Bishop Pass via the Sierra High Route over Knapsack and Potluck Passes.
