Bleeding master cylinder

None of what I have read so far takes into account that the air might not be in or close to the master.
Sounds to me like you have a good handle on what the issue is, and I have used a squirt bottle with a hose on it to force the fluid up to the master from the wheel cylinder end.
It works well when you are doing the bleeding by yourself.
FYI, it's ok to only fill the master half to 2/3 of the way also because it helps keep the fluid away from the cap a little better.