My max is 7 days also so I don't have any surefire recommendations. 

As a slightly amusing illustration of what not to do, a guy my kids met on the JMT this summer had heard that re-supply on the JMT was a PITA so his solution was to carry two bear cans both filled with Tofurkey dogs.  His pack weight was apparently around 80#  🙂  No idea how that worked out for him since he was just starting out.

Doing a rough calculation, say you need 3000 cal/day and you can find food that averages out at 200 cal/oz (nuts, fats etc),  you need to carry 3000/200 = 15oz a day which for 11 days is 165oz or about 10.2 # plus the bear can which seems feasible assuming your base weight is ~30# and your  pack is up to the task of carrying ~45# or more comfortably  

Taking a real food, a serving of Costco walnuts are about 200 cal per 30g and there are about 45 servings in a 3lb bag with is 3 days of calories.  You need just under 4 bags for 11 days and I haven't tried it but I think a BV500 will fit 4*3lb bags of Costco walnuts which 12 # plus the bear can. For weight and calories that also seems feasible. 

The trick then is to find a variety of food that is as compact and as dense in calories as walnuts that you can stand to eat for 11 days. 

Note that Bearikade have an expedition bear can that is 900 fl oz which you can rent or buy.  That may allow for some less dense food.

Another resource is that some wilderness campgrounds in SEKI have bear vaults so if you plan the first part of you trip around those you can carry the remainder of you food outside the bear can and place it in a bear vault at night.

Some people use Ursacks but I don't think they are are approved for the National Parks...certainly not Yosemite...but you could use one in addition to a bear can for the remainder food intending to place it in a bear vault but then having a backup in case the bear vault was not available or you get delayed.

From this it seems the bag hanging method is allowed in SEKI so a simple food bag might do.

Another way I have heard of is to arrange a rendezvous with a packer around the halfway point of your trip.  That will be expensive unless you can share the cost with others and you will need to be there on time since I believe caching is not allowed.  However if money is not a problem for you this is probably the most pleasant option.