I am working on a project with this exact same spec requirements with this exact same problem.
I honestly think the specs requirements are incorrect. I've seen a few of these forms, the spec part is always pretty much the same. I'm hoping it's more of a suggestion than a rule. I'm about to deliver an MP4 with the codec, dimensions and file size they require.
I'll try to follow up and let you know how it turns out. If I don't follow up, either everything was fine and I forgot about it, or they killed me and I'm dead.
yes you can make a .mov at this size, you are just going about it the wrong way.
i personally never render to h264 out of AE.
a better workflow is to render to an imtermediate format like prores and then do the compression after.
some tools put restrictions on making h264 files that are in .mp4 containers because there are guidelines that are supposed to be followed
anyways... render out to prores. drop in to mpeg streamclip and export to h264. it works.
i havent tried it in AME but that would probable work as well, just dont try a .mp4