Under Round Earth Theory, Relativity states that the force of gravity, in higher concentrations, will have an effect on the passage of time. It also predicts that the force of gravity varies over the Earth's surface, which means different parts of the Earth move at different speeds, and accelerate at different rates (as circular motion is acceleration). This is the flaw they point out in Universal Acceleration, why do you not note it in your own theory?
Why has the earth not torn itself apart, if it is round?
This is a fairly intelligent question formulated in the an almost in-cohesive way
Short, simplified answer ... time dilation is not the only effect ... relativity also says that space is contracting (Lorentz contraction) ... so ... if you move faster your time runs slower but your distance also shrinks, so for the outside reference you move with the same velocity. The earth is saved ...
The famous spaceship travelling ... from the outside's frame of reference it moves according to the right speed and across the right distance to its target, but inside the ship the time dilation results in less time passes - but the distance is also shrinking and so it arrives at the same target and nothing is torn apart.
I found a website were someone actually calculated the stress that should exists due to that very idea ... about 5 meter difference per year. Of course, its a site that claims relativity to be a conspiracy ... it does not consider length contraction.
I am sure someone with deeper knowledge of general relativity can give a more profound answer ... especially if we go into issues like the Bell's spaceship paradox or the Ehrenfest paradox (which actually brings up a few issues on rotating objects and geometry) ... all of these problems are complex but are solved under general relativity.