Well, I'm going to simplify this a bit. Deer(and everything else) are killed by the diameter and passthrough. Diameter(expanded, if that applies) is what determines the overall diameter of tissue damaged.

Passthrough is important because of the length of the wound channel, and because exit holes bleed much more than entrance holes.

So, you need to find atouger bullet which will exit. Your bullet is exploding, which causes more damage where it explodes, but it carries a much smaller diameter to it's final resting place. It also causes it to not exit. Lowering your powder charge might help. Pellets will never give ideal results, theye are just easy. They are too coarse. Try loose powder somewhere between 100 and 150 grains. If you lower your charge down, the current bullet might hold together and exit on these close shots. With "quick loaders", you can load as fast as pellets and be more acccurate to boot. Also, you might look for a bullet designed for higher velocities.