Lets go back to the OP: nobody argues that you would need a humongous push to keep Earth accelerating at 9.8 m/s/s. If this was done with chemical energy, the weight of Earth would have to be spent every few seconds, so Earth would have to start weighing what modern science believes millions of galaxies weigh.
Even if the energy pushing Earth was nuclear, millions of times the weight of the Flat Earth would have had to be spent to push Earth for four billion years.
This argument alone would be enough to put all Flat Earth hypothesis on the back burner of science; although you can argue that some totally unknown source produces energy that comes from nowhere, and that some unknown shield protects us from being fried by this incredible "engine" that pushes us, and that some strange shield prevents us from detecting such an inferno on the rims of the flat Earth, and that some strange phenomenon makes that such a rocket produces perfectly smooth, controlled power, this is too close to madness to even consider.
Now, if you want to entertain this idea, just for the sake of it, you still have to accept that the stars, planets, Sun and Moon are all in the wrong places and the wrong apparent size and brightness almost all the time, and so many other problems... better just forget FE.