Tell us about yourself!
Did you use whatever tire you had available because it was basically free? If you come across a 'space saver tire' do you think the lower amount of starting and stopping force required would be worth the effort to change-over?
Have you tried modifying cardboard tubes to try and accomplish the same thing, or soda cans with the ends cut off?
This type of thing encourages critical thinking, observation, patience, and a bit of research and communication. This is a well-rounded fun exercise in training the mind for anyone. Your story should be written-up for the Reader's Digest. Beside the 'make' itself, I found the story itself, riveting - and you might recover some of the cost of the build, back.