I believe most theories to where they run after the shot, (downhill, to water, circle back around) are just that...theories.
You can make a case for all of them (they do all of the above).
Let's face it, they run to where they feel safe.
You are just going to have to continue your grid work and go as far as you can.
Listen for crows and look for circling birds.
You are right, the meat is gone, however you can still do the respectful thing by doing all you can to retrive the carcass.