In your first equation F=ma, you cannot substitute B +1/E for acceleration a. This is because  acceleration must be in the same direction as force. In the case of gravity, it is towards the center of the Earth.
But you are saying that Gravity does not exist. That means
Assumption: There is no force towards the center of the Earth.

And you are saying the acceleration is due to the Electric or magnetic field. Now think about where the Magnetic field is directed towards. In the case of Earth, the Magnetic field is way stronger than electric, so I will give my analysis in terms of Magnetic field. So, we know the magnetic field points towards the Magnetic north (which is the geographic south pole btw). That means we should be accelerating towards the south pole if Magnetic field is the only force we are experiencing. (remember we said gravity is out of the picture). But we know that there is a force that pulls us towards the center and thus it cannot be the Magnetic force.......
Hence by contradiction, there is a gravitational attraction after all.

Peace.