MooV error - please help!

Question

I am working on an After Effects project which I received from Japan.  The original editor worked with a PC, and there is a good number of .avi files which I am having trouble with replacing.  I have taken the .avi files and converted them all to .mp4 (h.264) using a PC.  I used Adobe Media Encoder to convert.  When I went back to the AE project to replace the .AVIs with .MP4s I got this message in the picture below:
I tried converting a .mp4 file to .mov (Apple ProRes 422 (HQ)), but I still got this message.  I can upload the .mp4 files to the project if I just "import file" and not "replace file."  The .avi codec was Canopus HQ.  I need to keep this project the same, and can't just upload new .mp4, sine I don't know which parts of the .avi files were used.  Is there a solution so I can replace the .avi to .mp4 (or any other type that might work)
EDIT:
I have tried all of the suggestions from the link below, and updating QuickTime, but nothing is working:
http://blogs.adobe.com/aftereffects/2013/08/solutions-for-problems-with-quicktime-files-in -after-effects-cc-12-0-because-of-conflict-with-dvcprohdvideoout-quicktime-component.html
Mac (computer with AE project)
Operating System:  iMac 27", Late 2013, Mac OSX 10.9.1 (Mavericks)
Software:  Adobe After Effects CS5.5 v10.5.0.253
Processor: 3.2 GHz Intel Core i5,
Memory: 8 GB 1600 MHz DDR3
Graphics: NVIDIA GeForce GT755M 1024 MB
PC (computer with Media Encoder conversions)
Operating System:  ZT Systems, Windows 7 Professional
Software:  Adobe Media Encoder CS4 v4.0.0.374
Processor: Intel Core i7-2600 CPU @ 3.40 GHz 3.40 GHz
RAM: 16.0 GB
System Type: 64-bit Operating System
Other
External HD with AE Project:  Western Digital "My Book Essential", Capacity 3 TB, Format = Mac OS Extended (Journaled), USB 3.0    
External HD with .avi and .mp4: (unsure what brand), Capacity 1 TB, Format = Windows NT Filesystem (Tuxera NTFS), USB 3.0
External HD (unused, plugged into Mac):  Western Digital, Capacity 6 TB, Format = Mac OS Extended (Journaled), Thunderbolt
QuickTime Player v10.3 (727.1)

Answer 1

It's odd that files you're creating in the Adobe Media Encoder are not being read by After Effects, even though they're different versions.
Does AE on the Mac not read the AVI's?
Unless you're running out of hard drive space, you shouldn't worry about the file size of the assets you're using in AE; it has no effect on the file size of your finished product.
If, however, you must make them smaller, I'd suggest using a better intermediate codec. One that doesn't lose data and one that AE finds easier to work with (it's very hard under the hood for AE to deal with codecs that use inter-frame compression). DNxHD and Cineform are both excellent codecs (free from Avid and GoPro respectively). They're not totally lossless, but they're visually lossless which is good enough for most work (and worlds better than H.264!)
If you don't want to go with a professional 3rd-party codec, try Quicktime with the PNG codec or, if you must go smaller, Quicktime with the Photo- JPEG codec.
Speaking of third-party codecs, you haven't installed any codec packs on your system, have you? I have sometimes seen some of them wreak havoc on professional video applications.