I think it would also require that gravity doesn't obey the inverse-square law, so stays constant in magnitude throughout the entire vertical component of the t

I think it would also require that gravity doesn't obey the inverse-square law, so stays constant in magnitude throughout the entire vertical component of the trajectory. An infinitely-flat earth would also mean the force vector points straight down, instead of shifting slightly to point to the earth's center of mass across the horizontal component of the trajectory.