Wow, that's a lot of screen caps!
But there's one crucial piece of information missing: what are you expected to deliver? How will your AE work be used next?
You should also be made aware that making H.264 video really isn't AE's strong suit. If it were my video, I'd render a lossless file in AE, and use something like Adobe Media Encoder to do the compression.
My work in AE is the final video and it is intended for the web.
I tried a lossless export and the result of that is that I have a gamma shift directly.
Also, I ran into this thread
Where Todd Kopriva says that :
"The QuickTime format can now contain an embedded ICC color profile. But After Effects doesn't know that. There's a feature record in our database to make it so that After Effects does know about this and can embed an ICC color profile into a QuickTime container; I just called the person responsible for that feature and suggested that I thought that it should be a higher priority for future development. So, there's no need for you to file the feature request."
And my video is kinda like it has a profile in it that only Quicktime sees. Not the others players.
well I am confused ...
Personally, I wouldn't fool around with those color profiles unless I KNEW I was using footage that required it, and I wouldn't use it when rendering unless I knew that the delivery specs required it.