Thanks to posters who offered advice on running at Disney World. Here is what I found:
Yes, running DOES suck at Disney, but it can be accomplished. I managed to get 10/day in, but it was very boring and the weather was atrocious (hot, sickeningly muggy).
We stayed at the Disney Boardwalk resort and what I did was simply run circles around the Boardwalk path. It is approx 0.83 miles (measured with my Forerunner on day 1), so I would do just over 12 laps each morning. This wasn't terribly easy, because of the bridges at each end (and it was the muggiest time of day). Many other runners were doing the same thing. I opted against the so-called "running path" because it was basically a very winding sidewalk that passed through a lot of heavily trafficked driveways.
I'm sure many other similar opportunities exist there, so people traveling there CAN get their miles in. There are also many "gyms" there with decent treadmills, so this is another option.
So......Running in Disney is possible, albeit a bit boring. If you travel there, be ready to suck it up and deal with it for a few days. I was very glad to get back to my hilly, rural roads and decent temps and humidity.
Just thought I'd post this as advice to anyone else who might be wondering.