Is this something new (that all BC rooms have the daybed)? My belief was that not all Epcot resort rooms have the extra bed (it's only a request) which is why our family sadly has outgrown the BC. We had many, many great years of staying there (Epcot resorts are awesome location), but the daybed is simply a must for us now that our kids are a bit older.
If it's the Epcot resort area you really want (which I don't blame you, especially with the ages of your kids and Espn Club being right there too!), then maybe price out a deluxe room which I believe would be club level which would be a GREAT perk for your family make-up (extra space in the lounge to spread out).
Also, I know nothing about Swan and Dolphin except that they are located right in the Epcot resort loop. Maybe those rooms have a daybed to give you 3 beds?
If none of that works out, I'll bet your sons would like CR or Poly, and you'd be guaranteed a daybed in those rooms. If you had two 20-year old GIRLS, then I'd think twice about all sharing one bathroom (lol), but with boys and the larger size of these monorail deluxes, I'm pretty sure you'd be just fine.