Understanding / troubleshooting After Effects crash
It sounds like AE is encountering a point in one of your source files where there may be corrupted data, and while the file might be playable within the AE/PPro canvas, exporting isnt possible because of the way AE reads the file. 

I don't see why using Media Encoder would be any different, they are built around the same engine. 

I would suggest trying to replace the file you think is the issue with a proxy (same resolution) rendered using another application, perhaps VLC. Another option, would be (you mentioned 6:51 timestamp), is to split your clip in Premiere on a Sequence. Splice 10 seconds before that timestamp, and 10 seconds after. Render 2 separate files out, and drop them in. 

This will leave a black hole, which you would have to fill... But that would tell you if the source file is the issue. 

Lastly, clear cache, and also you could try accessing the hidden secrete menu in Preferences. On windows, hold Shift and while holding, click Edit - Preferences. There will then be a new "Secret" tab that allows flushing of memory every X frames during output, and some other options. 

My guess, bad source. Have to work around it by either re-encoding the file into a format AE likes, or splitting if you can.