the default output module for ae will render a quicktime with lossless animation as the codec. this codec is an intermediate codec, designed to maintain the highest quality when going between various stages of production and is not intended to be for final playout.
what you should do is take that huge .mov to a compression utility to create the file that you need to final playout. adobe's media encoder, apple's compressor, quicktime pro, or any number of other compression apps that can do multipass encoding will do a good job of compressing that file down and maintaining a fairly good level of compression.
a free app that i use often is mpeg streamclip. drag the .mov in, then choose export mpeg-4. enable multipass and b-frames and set auido as needed. if you have a target bitrate that you need to meet, you can enter that, then just click 'make mp4'.