The sea is not squashed because it is an in-compressible fluid. The air has a density profile because it is a compressible fluid.
The important part is that they are both fluids. IE, you can have things float or sink in them. Compressibility is just a red herring that you have decided to introduce.
Ah-ha! There's a significant difference in there! The Earth's rotation has a constant speed, it does not change every second. Therefore, no crosswinds would be expected, and indeed, we don't have them.
We don't have them because the air is moving at the same rate as the earth. Exactly as the air accelerates at the same rate as the earth. No delta. No rate of change. No perceived movement. I believe a young Jewish lad once called this 'relativity'.
Relativity has no relation to what we are talking about here. This is something Newton has described as "inertia" long before Einstein. You are right, though, there's no rate of change, no Delta, that's why we don't feel the "1000mph" crosswinds you said.
But, in order to account for gravity, you introduced a rate of change, a Delta, of 9.8 m/s² on Flat Earth's upward velocity. That is the problem, if it described reality, we would feel it.
In the Round Earth model, the Earth does not accelerate at all! And that's the reason we don't feel it.
Acceleration is, by definition, a rate of change in something's velocity, and thus, your explanation for gravity in the Flat Earth model is flawed.