Parsifal, your explanations of UA have enlightened me to how it works. From what I understand, UA explains the bulk of the force that we feel on Earth, while gravity contributes to the observed local variations.
However, if one admits that the experiments verifying gravity were not faked/manipulated and have been repeated several times, then what explains the unusally
small gravitational force as predicted by UA? These experiments verified that, at least on a small scale, that the gravitational force is proportional to both masses and some constant. Of course, there's an easy way to explain this: not unlike Newtonian mechanics and its relationship with SR, the proportionality is merely a small-scale approximation of effect, and gravity is much less strong than predicted at large scales.
But this would entail completely rethinking the orbital dynamics of the various bodies interacting with one another. I admit I haven't done the calculations myself, but changing the gravitational force between objects orbiting in complicated systems should result in deviations from observed behavior. I guess by denying the given mass values of objects in space and positing new ones one could make everything work out, but then there's another problem: such mass values would be wildly inconsistent with the assertion that stars are big balls of gas with certain densities. So you would have to change the composition of the stars and fudge around with the Ideal Gas Law (maybe say it doesn't hold for high temperatures?) to really make this work. Then you would have to reconcile this with spectral evidence detailing exactly what gases are in the stars. It turns into something really bad.
I also don't see why we have to resort to this kind of physics to disprove Flat Earth. The geometry simply doesn't work out, as anyone can figure out by simply measuring a triangle on the Earth!
Here's an interesting (and fun) experiment to check that Earth isn't flat. You'll need an airplane and a very accurate compass. Head due West for 50 miles. Then head due North for 50 miles. Now turn to where you started (ensure that you won't miss!). Record the angle turned in your notebook. When you arrive where you started, record the angle from due West in your notebook. If you sum all of the angles in the triangle, they don't add up to 180 degrees
In fact, they add up to more than 180 degrees, proving that the Earth has a curve to it (and not the weird one).
Now as for things that I haven't seen an FEer explain (and I apologize if it's on the Wiki; I've tried my best to read it):
The "shielding" aspect of UA -- what's the physical mechanism behind this and can this be quantified? Also wouldn't that planets/stars in space have halves that shield the other halves, yielding some interesting math? I presume that the math could eventually work out, unless some other Round Earther can prove it wrong to me.
https://en.wikipedia.org/wiki/Schuler_tuning. This is used in virtually all software written for inertial navigation systems. Without it, they would deviate drastically. Current inertial navigation systems are rather accurate (still pretty poor) and can be used on things like ballistic missiles. Why would inertial navigation systems include something that shouldn't exist per FE theory?
The Foucault Pendulum. I'm aware of the page on the Wiki. Dr. Samuel Birley Rowbotham clearly has no idea what he's talking about as numerous Foucault pendulums have been built with differing materials and many in climate-controlled environments. They all confirm one another. I've seen one in a museum. One cannot attribute this to simple environmental conditions. As for the second part, Mach's principle is misinterpreted. It's a general heuristic about making physical laws relating the stars to us -- by observing the motions of the stars, we can perhaps conclude something about our frame. You can see this in GR where the metric tensor (spacetime) is affected by matter. It says nothing about the stars' gravitational pull moving the Foucault pendulum (which would be totally inconsistent with the idea of a weak gravitational force!). One should note that there is a current debate about the idea of "absolute rotation"; this has little to do with a Foucault pendulum or FE.
Seismic science. I'm not familiar with this topic, but it seems that seismologists determine the composition of the interior of the Earth by examining reflected seismic waves. You'll need to discredit their observations.
Pictures by amateurs and commercial ventures. Rockets work in space (that's a fact and if you want to debate that, I suggest you read up on physics). The ability of them to get to space is consistent with Newton's laws. There have been pictures taken of the Earth that clearly show that it is round. Many different types of cameras have been sent up, including those without a fish-eye lens. They have verified that the Earth is round.