Humber,
Imagine that (with some supernatural being's help) we've arranged for the following idealised testing environment:
Earth has been essentially replaced with a giant billiard ball, thus having a perfectly flat surface (insofar as we use the term "flat" on earth), but it still has essentially the same size, mass, and gravity, as the earth, plus an atmosphere that is similar in terms of composition and so on. Let's say the rest of universe is completely empty. No sun, no stars. (But we'll allow ourselves torches or similar so we can see what we're doing!)
We've also arranged so the southern hemisphere can rotate independently of the northern hemisphere - as if the earth had been cleanly sliced in two through the equator and then the two halves put back together again with a frictionless interface between them. You can imagine a long shaft running through the north and south poles and thus joining the two halves if that helps but shouldn't really be necessary! We also have things set up so the southern hemisphere is rotating (from west to east) slightly faster than the northern half so that a person standing just south of the equator and looking north will see the northern hemisphere apparently moving right to left (east to west) at 10 mph, even though the northern hemisphere is still rotating at the usual earth rate - something close to 1000 mph at the equator if my quick calculation is correct.
In addition we have a perfectly smooth and constant speed air flow moving around the globe from "west to east", at exactly the same speed as the southern hemisphere at the equator but also sufficiently far to the north and south of this also for the purposes of any cart testing we may want to do in that area. So this air flow is like a belt around the earth's equator and it's speed matches the speed of the ground in the southern hemisphere in the equatorial regions.
I'm presuming that you're happy to accept that the slight curvature of the earth's surface, and similar very small effects that come from that (plus missing stars and sun, etc) are not significant enough to make a difference in terms of testing a cart like spork's on this version of earth. But please tell me if this presumption is incorrect, and if so what the problem is. I agree there could be extremely minor effects, or difficulties with getting the "perfect test environment" from some of this, but I haven't seen you raise this earlier so it seems likely that you agree we can ignore these issues unless unless perhaps we ended up looking at a cart where the difference between possible success and failure of some test was extremely small. Spork claims his cart can comfortably beat the wind, so that doesn't appear to be a likely scenario. We're not using General Relativity either are we?
Finally, let's say you are standing right in the northern hemisphere, close to the equator, and I am standing near to you (for now) but on the southern side of the equator. We will be moving relative to each other though because the two hemispheres are moving relative to each other. We both also have a spork type cart, exactly the same in every important respect.
Before we move onto testing the carts, can you please confirm that this description is clear. Please tell me if you would feel any "real wind" where you are standing in this idealised world (just north of the equator), and in which direction and speed it might be blowing. And what would I be feeling at my position just across the boundary in the southern hemisphere? Is that "real" also or not? Does any of this set-up suffer from the problems that you see with the treadmill tests?