After some discussion with the folks at fccinfo.com, I've learned some things about the FCC data for cell sites. First, the data on the fccinfo.com is the same data that's available from FCC.gov pages. Second, cell towers only need to be registered with the FCC if they are 200' or taller, so this is why the FCC data leaves out so many cell sites. Most cell sites are on buildings, water towers, fake trees, etc. and most of these are far less than that 200' height, hence not registered with the FCC. Lastly, the FCC data doesn't specify what type of site it is, cell, TV, radio, etc., so there is no way to tell from the FCC data what type of tower it is.
So we are back to the drawing board on finding a better source for cell tower locations.