This is a good question, and I may have found an answer. In the Output section of Properties, choose H.264 as the format from the drop-down, and H.264 under Encoding. Then check the “Lossless Output” option that appears – this seems to be available only with H.264. I loaded one of my .mp4 videos made with Handbrake, and using the default settings in Blender, the VSE output an AVI file of very high (I venture to say nearly identical) quality but at a higher compression ratio.
For your additional video I recommend creating high-quality .mp4 to edit in with your Gear VR strips, to insure consistency. Or you can be adventurous & mix things up. Audio is encoded separately using different codecs so will not affect video output.
This seems to be as close to a thoughput treatment as I could manage, though there does seem to be some re-encoding given the file size difference. Then again, I used Blender’s default specs for bitrate & the like, which were much less than I put into my .mp4s for uploading to Vimeo. So setting higher quality parameters should insure even better results.
The only drawback may be the .avi container that H.264 uses – I could not find a way to change that. But since it’s just a container format, it shouldn’t present issues (crosses fingers & knocks on wood).