Techie is right on. You don't say what that 200' of cable is but I can guess and there's your problem. Those little drop amps are not going to help you. You are in trouble here also because you are not dealing with a cable company that is used to dealing with long runs of coax. This is Verizon FiOS and about all they know is running a few feet of RG-6 from their ONT on the side of the house to the sets. I even wonder what kind of test equipment they have and without that it's like a blind man driving a car, especially in your situation.
So, what I'm saying is this is not going to work with that cable. I too recommend .500 hardline. You are still going to need at least one amplifier and because you need to have reverse gain also things get tricky. This is not something you are going to do without proper tools, test equipment and some knowledge about what you are doing.
Then again I wonder if this is something that should even be handled on this level. Might it be better to have Verizon just provide another service to that building?
-Hal
