Jogging stroller
It's funny. Prior to a couple of days ago, I had never seen this. Then you asked your excellent question. Jogging stroller.
Maybe a couple of nights ago there was a news story about a guy doing this killer road walk, maybe coast to coast. Anyway, he was pushing a jogging stroller full of his gear for the trip.
Then today, I see this fellow along the Charles River while I'm enjoying the early afternoon paddling my Wildfire. He appeared to be pushing all of his worldly possessions around in - you guessed it - a jogging stroller. Much better than a shopping cart.
Anyway, you should be able to rent a jogging stroller somewhere. Those things are really smooth and so easy to push a pertty heavy load. We have kind of a modular baby chariot and the company sells a sort of rickshaw attachment that would work well, but I don't we'll ever get into that.
Hope that helps . . .