I have personally flown from the US to China, and experienced a roughly 10 hour time zone difference. Since this was late spring in the Northern hemisphere, that means the sun was overhead in one of the two places at all times, clearly violating the "sun passes under the Earth" model, assuming daytime in Chicago occurred at the same time when I wasn't there as when I was. (Since daytime in Chicago is fairly predictable, I can't imagine it would have changed simply because I was traveling.)
The conspiracy cannot explain this, because even if there was a gps unit and microchip in my watch telling it to mess around its reading depending on where I was in the world, it still wouldn't explain why my internal body clock differed so greatly from the solar time in China.
If you remove that part of the hypothesis, then this model becomes almost identical to the standard FE accelerating upward model, in terms of observables. Almost but not exact because there would be a coriolis force, but if we assume a very large radius, this force could be made arbitrarily small, and therefore undetectable. (Conversely you could confirm this model by observing such a coriolis force, but I doubt you will.)