While it is possible, there will be certain things that will be hard to get at AKV if you don't own there--concierge and possible value rooms.
If you are on the fence and want to stay BLT some times, but mostly at AKV, you will be able to buy both through Disney. Some have done that--split the contract between both resorts.
For example, say you want to do BLT every 3rd year, with AKV the rest of the time. Buy 1/3 the points you need at BLT and the rest at AKV. Then you will be able to use banking and borrowing situation to accomplish both.
As others have said, the difference in price between AKV and BLT with Disney is at least $8.00 per point (and bigger if you go resale). It will take a while to make up the point difference. If your goal is really to stay at AKV, then I would start out owning there. To me, there is nothing worse than owning points and finding out you can't stay where you want. And, as you said, your points will not go as far at BLT as they will at AKV which means you have to book a smaller vacation to start at your 11 month window and hope that what you want is there at 7.