Hi John!!!
I can totally relate with wanting to make sure you have your bases covered with your children and the amount of walking that can be done at Walt Disney World!!!
My suggestion would be to rent a double stroller at each of the theme parks. I don't think that your 4 1/2 and 7 year olds will be too big for the
Disney Strollers. The double stroller would give them each an opportunity to sit, and even nap, whenever they felt the need to.
The price for a double stroller is $31 per day. There is a multiple day rental available that reduces the price to $27 per day. The link above lists out important information about the strollers, such as rental locations, prices, etc.)
I definitely think this would be your best bet to ensure your girls have a fall back plan in case the walking catches up with them and they need a break from the walking!
Have a magical trip!!
Scott