Another vote for the 2BR at Kidani. The bus ride to MK is really not that bad. My DS7 has always loved riding the Disney buses, so he doesn't mind the ride. The pool and splash play area are great for the two kids. Plus, you will have the animals! The full length balcony at Kidani is great, compared to the small balcony at BLT.
My son always did naps in the stroller at the park, so we never had to deal with going back to the room for a nap. Unless you are taking your own stroller, you may want to look into renting from one of the local stroller rental companies. We have used Magic Stroller and Kingdom Stroller in the past. Both provided excellent service and comparable pricing.
Depending on how long you will be there, you could consider 2-3 nights at BLT in a 1BR and then switching to Kidani in a 2BR for the remainder of the stay. Split stays have their drawbacks, but it would be a way to be close to MK for a few days and then get the larger room for the rest of the stay. Who knows, with a split stay, perhaps you have enough points to squeak out a 2BR at both.