I brought my 10 year old umbrella stroller on our recent trip, just in case.

The thing is a hunk of junk, probably cost $10 ten years ago.

Saved our trip, really. It was fabulous when Mr. "just 4" passed out and way better than a park stroller, it saved us several times at the end of the day, which is not a time that I want to carry a sleeping 38 lber. Since we were on the monorail to Epcot and walking to MK, he went from park to bed at least twice without waking up.
I thought my 7 year old would wear out too, but she was a trooper, only complaining at the end of the trip at the end of the day -- and then only a little. Adrenaline does wonders ... she was having a blast!
You know your 6 year old best. If you are staying at a monorail resort, I would definitely consider buying or renting a double stroller that you can have with you from the beginning of your trip to the end, instead of a park stroller.
That said, we used that umbrella stroller all the way home. We had a late flight and put him sleeping from the plane to the stroller, through baggage claim and out to the van without waking him. It was wonderful. And cheap!
