Some thoughts... or options.
1)You can get used strollers cheap at resale stores, garage sales, and newspaper ads. Perhaps you know someone who could loan you one too. I still have both our strollers and my youngest is almost 6.
2)You can have your DH run for the car and pick you up. I have done this at other parks but never WDW, but I assume it is possible. Thus eliminating part of the walk.
3)Rent at the parks, or better yet scout for someone returning one later in the day and 'buy' it from them. I have done this at WDW. Not sure if some people might think this is unethical. Combine this with option #2.
-another rental perk is that Disney will replace it if it dissapears. So it is safe to leave it for long lengths of time in one of the stroller parking areas. When we went to DL last summer we parked Just inside of Toon Town and left it for about 4 hours because it was such a hassel in there (so many little people darting in front of you, plus gridlock). It was still right where we left it when we were ready to leave Toon Town, but if it had gone missing I could have hoped on the train and gotten a new one up front no problem (just keep your reciept on your body).
4)Buy a $10 cheapie stroller and use it to carry everything but your child, making it easier to carry your child. We have found this the best part of having a stroller. The other benifit to this option is if you don't need to 'use' it you can fold it up and just carry it saving yourself the hassel of trying to push it through crowds.
5) Use fast pass whenever you can. Even for rides with shorter wait times (some people only use fp if stand by is over 45 mins) because if standby is short then fp is really fast! It seems like the standing still in line wears my kids out 3 times faster than walking around. To avoid the extra walking and backtracking FP use can cause don't all go to get them, send DH on a missiion with all your tickets in hand.
We always do this. The kids can walk slowly and look around with you (and get autographs), DH runs to FP ride, gets FP's for all, and doubles back to meet up with you! For us, by the time we reach the FP ride it is often our return time already!
I hope this helps. I have two bigger/older children who are still a bit young for all that walking. We will be bringing our stroller when we go to WDW.