Well, I have no horse in this race myself since I never used a swap...
But, as someone who routinely rents a scooter from companies off-site, I wonder whether anyone has explored this as an alternative? I did a quick search on Google for
stroller rentals in Orlando and came up with several...
for example,
http://www.orlandostrollerrentals.com/ has a nice double stroller that is $85 for a week. As with scooters, the company will deliver to your resort and pickup.
I realize it's not as cheap as a swap, but as a scooter renter, I have always gotten great service and been very pleased with the quality of the equipment. And as is true for scooters, as well, the price certainly beats Disney!