Major issue importing and exporting mp4 with AE and Media Encoder
Hmm very strange, never seen this before. Here are some things I would try to figure out what is causing the issue:


Try re-encoding the file with ffmpeg into both the same container (mp4) as well as other containers such as .mov, .mkv, .wmv, etc. Maybe there's a problem with the codecs for Adobe on your machine.
Which version of AE and Media-Encoder are you using? (is it a legal copy?)
Have you tried uninstalling all codecs such as quicktime, etc. and reinstalling them?
Have you tried uninstalling the Adobe software and reinstalling it?


Since you said that on draft quality the preview looks fine momentarily, I assume that the problem is rooted in the Adobe-Software. Maybe switching off hardware-acceleration might also do the trick. Make sure to keep us updated, I'm genuinely interested what's causing this weird issue.