So I'm trying to render a composition in H.264, constructed from .MOV files and .AIF audio files.
So that's not the best way to do it.
Here's a post that I wrote so often on the Creative Cow that I made a cut & paste version:
Dave's Stock Answer #3:
Don't use AE to compress files for final delivery. The various compressors are there only to make quick 'n dirty files showing a project's progress to producers, clients, the kids, etc. AE is incapable of doing multipass encoding, a crucial feature that greatly improves the image quality of H.264 and MPEG-type files in particular.
Render a high-quality file from AE, and use a different application to do the compression. Popular ones are Adobe Media Encoder, Sorenson Squeeze and Apple's Compressor, which comes bundled with Final Cut Suite. Even compressing in Quicktime Pro is better than compressing in AE.