As a physicist and round earther, I can confirm that an object can constantly accelerate while never reaching the speed of light, and that that would satisfactorily explain all phenomena we observe.
From a stationary reference, the Earth would appear to accelerate at 9.8 m/s^2 at first, but as it got faster, its mass would seem to increase, and things on it would seem to slow down, and the acceleration would appear to drop off as its speed approached, but never reached, 3×10^8 m/s.
From the Earth's reference frame, it would just feel as if we were constantly accelerating, though our measured speed would always, of course, be zero. Any stationary objects visible from the accelerating Earth (not that there are any in the FE model) would appear to accelerate down, while also contracting vertically and slowing down. Before long, everything would appear to be moving downward faster than the speed of light. This is possible because an accelerating Earth is not an inertial reference frame, so not all laws of physics apply.
The density thing, on the other hand, is not a satisfactory explanation. It's vague (What determines the rates at which things go up or down? Why do all things accelerate down at 9.8 m/s^2 in a vacuum chamber, regardless of the pressure in the vacuum chamber?), dependent on RE concepts ("Pressure" and "buoyancy" were coined by REers and explained with gravity), and worst of all, equivalent to gravity. I suspect if you did the math out and applied Newton's laws of motion, you would eventually arrive at a downward force on all objects equal to 9.8 m/s^2 times the mass of each object.