Don't worry about feeling silly riding around in an ecv. If you experience pain after being on your feet a couple hours than an ecv is going to give you a much better experience at disney. Plus, there are tons of people doing the ecv thing at disney, so you won't feel alone out there. I always wave to all the people in the ecv's as i pass them in the park. Some wave back, some don't.
You will most likely be able to be out and about enjoying yourself more during the day. Maybe do half a day, then a break, and the continue later. Some people can go the whole day without a break, but its a matter of preference.
Only tips about the bad back. If your short. I'm 5'1" tall. So, for me to reach the steering handle and to sit properly so i don't aggrivate my back. I bring a back cushion along. I also made a cover out of boat type material from joann fabric, so i could cover and secure the back cushion. That way i didn't have to bring my cushion with me for every ride, plus if it rained my cushion stayed dry. I wouldn't have left it on the
scooter because someone could easily pick it up, and well it would leave me in pain, so thats why i tie it down.
Jerky affect. If your in tight quarters, lines etc with the ecv turn your speed down as slow as it goes, people stop and start and if you lift your hand off the go handle you jerk and may aggrivate your back. So if your out in the open wide paths not lots of people feel free to turn up the power, but in close quarters remember to turn your speed down to avoid the whip lash affect.
If i wanted to get out and walk, which i do at certain times of the day when things are less crowded. I tend to park off to the side, sometimes in a stroller parking area.
Renting offsite give you access to the ecv at the resort, and to and from the bus stops to the parks, which can be rough at the end of a long day at the park.
Connie