This got difficult for you, then for us, when you envisioned it as having wheels on the sides of the box. If you had imagined one of those flat furniture dollies, but with a bigger area and an actual box on top, you would have had it.
For cheap, you might consider buying a Harbor Freight furniture dolly and stealing the wheels.
Also, these wheels ALL have axles, so you're lucky someone saw that this is the kind of thing that would work.
This won't work. The wheels need to be large and capable of rolling through grass. The furniture dolly wheels are too small/hard and the swivel feature means that debris will get caught in the wheel and they will fail.