Yup, sounds like the perfect solution to me! Especially if you are leaving the park... ride right around to the front of the park.
As far as the ecv us stroller vs people from Texas thing, there but for the grace of God.....
I'm not sure if this works or not - we were trying to go to Frontierland this past week from toontown, and we had to wait 15 minutes (for the parade to get out of the way)

One too many bad experiences with crowd control/pushing/rude guests. Also, when you get a claustrophobic person in those conditions, it's way too easy to start a panic. I was in that situation once where one person caused chaos and a lot of people got hurt.
....I think you should let Disney know about this experience maybe they should be monitoring the crowd level there during parades! That is NOT good....and hopefully someone complained that night but please atleast make Disney aware so they can try and take precautions 
If I have to make my husband push me in a wheelchair we will not get to go. And I can't push myself because of arthritis. So it's