I think that you had better look into a gas motor, as was on the old gas engine wringer washer, or a motor scooter engine for your wagon.
You will soon throw a hip out and cause even more pain pushing it with a leg.
Try Free Cycle for a wrecked scooter, should have all you need.
I suspect this idea, will be like some of mine, excellent on paper and not so good on the ground.
LOL Hot Rod Granny...
Yeah, I could soup it up and power it, but I really want to be able to enjoy the peace and quiet in the garden. Since I used to put one knee on my old American Flyer and push with the other leg, I think I should be able to put both heels into the dirt and give a little push. Just need to move it a foot or two at a time as I pick. Once it is full, I could pull it.