With respect to shots from dead astern, there is a need for the performance required for this shot to work. If I have fired my first round and the animal is now running straight away, I shoot; I don't wait to see what happens. My .375, .416, or .458 will drop him because the bullet has made it to the heart lung area of the chest while a .270 bullet is stopped in the gut. With a small bore making a going away shot on wounded game, the best you can hope for is to break a hip, which is not the most humane shot in the world, but it will bring things to a conclusion of sorts.
I consider 1000 ft/lb at POI a comfortable minimum for black bear, deer, moose, and similar sized game.
FYI
Factory Federal .270win 130gr sp still has 1050ft/lb at 500yd.
Factory Federal .270win 150gr btsp Sierra Gamekings still pack 1000ft/lb at 650yd.
IMHO if you are hunting for meat (and I hope your are!), consider learning to stalk or call your prey, so you will never have to take a tail shot and deal with the messy aftermath of a gutshot animal.

Failing that, bring on the RPGs and .50cals as drvrage said.