We are owners at AKV and love staying there. We bought in in 2008 and have added on 3 small contracts since our initial purchase. Our initial purchase was for enough points to stay in a 1BR for 7 nights during magic season once a year. Within 2 years we realized that we like to stay longer, since we are spending money on flights, and we like to bring family. Last summer, we did our first stay on the concierge level, and now we are happy that we have enough points to do that every once in awhile.
Since you find AKV appealing, I will focus on that resort. As others have pointed out, AKV does not have much of an 11 month booking advantage over other owners, other than for concierge level and value rooms. All of those rooms are at Jambo House. There are 5 2-BR lock-offs for each of those categories, meaning that at most, there are 5 1-BR and 5-studio rooms available at any given time. The 1-BR units at Jambo only have 1 bathroom. Many people are enticed by the low point cost of the value room and consider that as a positive feature to buy in at AKV, but you need to know that those rooms go quickly, often at 10-11 months in advance. With that said, you should make sure that you are calculating your point needs at AKV based on minimally staying in a standard view room.
AKV and BLT both have 2 bathrooms in the 1BR (and 3 in the 2BR!). The point costs for staying at BLT are higher for any given time of year, so you need more points to stay at BLT. It is difficult to get into BLT during some times of the year, but we have never had any trouble getting into BLT when we have wanted to stay there by booking exactly at 7 months. We have gotten a 2BR in early June and late July and a studio in mid-Oct (using a wait list). BWV and BCV are basically impossible to get from the beginning of Oct through early January.
Although AKV is perceived as "way out there", we have generally been satisfied with the travel times to the parks. One nice thing about AKV is that there are only two bus stops, and the park buses stop at Kidani first -- usually empty. BLT has one bus stop, but the buses proceed to stop at Poly and GF, which adds to the travel time. Travel to Epcot from BLT is a minimum of 30 minutes, and usually more like 45 minutes. So, although it is awesome to be able to walk to MK from BLT in about 10 minutes, it is a little bit of a pain to get to all of the other parks. AKV is serene and peaceful . . . BLT is frenetic and noisy. . . IMHO.
Given the size and ages of your family, I could see you quickly wanting to get into a 2BR. Who is going to sleep with whom? Will DS15 sleep with her little sis? Will the fraternal twins share a bed? Right now, a 1BR gives you a king in the master, and a full-sized and single hide-a-bed in the living room. Currently, AKV can be had on the resale market for between $60 and $65/pt. The larger the contract, the lower the buy-in per point. Resale for BLT is about 50% more per point and will probably drop in price more slowly over the next 2-3 years.
I would avoid trying to own at two resorts until you have enough points at your primary resort to do the things you want to do. We have done split stays using our AKV points, but they are kind of a pain. I agree with one of the other posters, you should try to find a contract with at least all of this years points . . . there are tons of AKV contracts out there. Resales with banked points are fairly easy to find for AKV, as well.
Finally . . . good luck making a decision. This is a long-term commitment and you should be happy with your home resort choice. Oh, and you need to update your children's ages in your signature!!