Aside from the issues that
@FortForever had just very recently getting all that installed (chronicled around here somewhere in another post) I honestly have never seen a company that rents those. Sells them... all day long. Rental? Not so much.
Are you staying onsite, or offsite?
If onsite, the answer is obvious - use Disney transportation. I know a lot of people come here worried about getting on and off the buses, but once you do it a couple of times, it's pretty much a non-issue, and the drivers are always happy to help; just ask.
If you are doing a "split stay" (part of your trip at WDW and part of it at Uni) then I have heard of people getting their rental vendor to pick up the
ECV and move it for them from one hotel to the other; obviously that has to be scheduled in advance.
If offsite, then the only other thing I could think of is to check with U-Haul in Orlando. They sell carriers, but a local U-Haul dealer *might* rent them - I truly don't know.
Harbor Freight sells a hitch-mounted carrier for $169; I suppose you could arrange to buy it in Orlando? Congratulations - you get to take it home as a souvenir from Disney World!
There are several places in Orlando that will be happy to sell and install a carrier for you, but I can't find a single rental vendor...
Let us know what you decide to do!