I have a few problems with your description of tides. Now I have to admit that I am a little hazy about this myself, but there are parts of your description that just seem wrong.
You make quite clear that the apparent absense of force in free fall is an illusion. The best example of this is if you jump out of a plane with scales glued to your feet, if you ignore air resistance you will appear weightless, but you are still being accelerated towards the ground.
You then go onto say that the centre of the Earth is in freefall. I am not sure how one part of a solid body can be in free fall without the rest of it also being in freefall. But this is not important, the bad bit is you claim that if you measure the gravitional force of the moon relative to the centre of the Earth and then define the centre of the Earth as having zero force then you get a negative force on the far side. This is a bit like claiming that if I define the gravitational force of the Earth at ground level as zero, I should be feeling a force away from the Earth on the first floor. Gravity always acts towards the centre of mass, it doesn't matter where you stand on the Earth the moons gravitational force is always acting towards the moon.
There is however another 'force' involved here, which you mention when talking about the effect of the Sun. That is the centrifugal 'force'. I know as another post has already pointed out in another post that this is not realy a force, but in this case it is helpful to think of it as such. If you include the centrilfugal force much of your description begins to make more sense. At the centre of the Earth, the gravitational force and the centrifugal force balance and it could be said that a body here has no force acting on it. Now a person standing under the moon will be subject to the same centrilfugal force, but because they are closer to the moon the gravitational force will be stronger than at the centre of the Earth and so they will be pulled towards the moon. Where as the person on the far side will again have the same centrilfugal force but a lower gravitational force and will feel a force pushing them away from the moon.
I realize I have gone on a bit here and I hope I have made myself clear.