RE: flat tires
I wonder if warming them would help. Maybe use a heat gun, and shape them a bit using a heavy glove to protect your hand? You might be stuck buying new wheels, or just living with them.
For the future, I saw some wheel chocks on a web site that lift the whhels off of the ground. They were nylon, and snapped on the axle. I cannot find the web site but made a drawing of the concept it used. It should be fairly simple to make them out of thin plywood or plastic.