I voted AKV, but I certainly understand the affinity for BLT due to location. You did not mention what time of year, as that may make a slight difference if using the pool is not an option. If you are there during swimming weather, I would sub-vote Kidani. The pool has a mini-slide and a zero entry and the splash play area is the best on property, IMHO. Additionally, although the ride to MK is longish, the buses to the parks stop at Kidani first and are basically empty, so you will get a seat for your little ones. Of course, the kids love seeing the animals. Kidani and BLT both offer the bonus of the third full bathroom in the 2BR, if you want to squeeze your group of 9 into a 2BR.
We have stayed at BLT three times, and love the proximity to MK. But we like AKV because when we return to the resort, we feel like we are away from the chaos of the parks.