I don't know about the casters that you are looking at, but there are certainly casters that can do the job from a weight perspective. Sinking into the ground might be another issue, but I think you could find some inflatables that would work. Try looking here, there is a solution but it may not be cheap.
Even if you have the wheels, it's not going to be easy to push up and down a ramp at 350# good luck! Interested to hear what you come up with.