I think you had better do some further checking. You have stated several potential problems. One is all the moderates, except Caribbean Beach (which has 340 sq ft rooms) have 314 sq ft. Normally the handicap rooms have a king-size bed instead of two doubles, and have a roll-in shower.
It is not too hard to fit an an
ECV or a wheelchair, but both, along with four people, could be a real problem.
I hate to suggest something that will add to your costs, but it appears to me that you might need to contact special reservations and explain the situation. It sound as if you would actually need two rooms; if so you need to make sure that they are connecting (which means there is a door which allows you to go directly from one room into the other) and not adjoining. Also, you might want to look into either the Contemporary or the Polynesian, which are 440 square feet.