Have you thought about a wheelchair or a roller this will give you something you can push and a set when need be. The down side is most can not self push but if you work in your feet my guess is you could walk a good amount of time and sit ( and have someone in your group push you when you need a break ) a wheelchair work well for this
If you have ever tried to push an empty wheelchair you probably wouldn't make this recommendation, that is a pain (although I know there are people who can do it, I am not one), a walker/rollator with a seat could work though, but Disney World is a lot more walking than most people realize. Somewhere around 6-10 miles a day. Yes, it is broken up, but that can be very hard, judging by the OP, I would say an ECV probably is the best option.
Yes, they can be a pain at times and yes, I resisted renting one many times myself, but my knees are finally at a point where I have to at this point. I am trying to get back to where I won't need to, but that is a long road no matter which path I take.
As for what company, I am sure you will get sick of hearing it from people, but still this point I won't ever rent from anybody but Gold Mobility Services at Disney World unless they are sold out for my dates. Seriously, they are that good. Their scooters are in excellent condition and the battery lasts all day. There were a couple of times on our last trip that I was leaving one of the parks and someone was limping along to the bus on the last bar of the battery on an ECV from one of the "featured providers" and they had charged overnight meanwhile mine hadn't dropped even one light and I was the runner for getting return times all day. The only park where mine did drop two lights was Animal Kingdom, but that park is hard on everyone. The other nice things with gold mobility is they have cup holders, fans, cell phone holder, under carriage lights and USB ports to charge your phone. These are overall small things that make things a little easier, but between that and the fact that they replace their fleet every 6 months, which means the
ECVs practically look brand new, you end up with ECVs that do get attention, but it is people commenting on how nice the ECV is and forgetting to give dirty looks or make nasty comments about ECVs. Seriously, it was the most pleasant trip we ever had with people in our party in ECVs and on this last trip we had three ECVs in our party. Our only issue was one person wasn't good at driving it, but that's not the company's fault. We did have one issue when entering American Adventure (which we had to enter through the exit due to the elevator breaking just before we arrived) where one of the ECVs refused to move after getting up the hill. I texted Gold Mobilitiy just before the show started, well before it ended they texted back how to fix it and said to let them know if it didn't work and they would be right out with a replacement, but it did work and never a problem after that. As a previous poster said, it almost sounds like a cult at this point, but compare that to
Buena Vista scooters who wouldn't do anything for us while in the parks when we had an issue and didn't care that the battery was in such poor condition that it wouldn't even last half a day. And on this last trip all of the other rental companies looked like they had been through the war and back, especially from the featured providers.
So, there is the extrodinarily long winded response as to why Gold Mobility over everyone else.