First of all, the animal couldn't care less if someone treats its corpse with respect--it's already dead, so I don't see how the animal benefits from this. Second, I'd say that the negative effects on the killer's mind from the act of killing far outweigh any positive effects from mindfulness in handling food produced from the kill.
Killing desensitizes, you become accustomed to taking life from another sentient being. The meat industry is likewise taking care to use every edible part of the animal, they're not producing any waste as far as that goes. Further, I don't think eating everything in the plate is making any measurable difference in terms of total meat consumed (if that's the implicit idea behind this). It's like the “think about the starving children in Africa” routine, which never made sense: people in Africa aren't starving because kids in the West aren't eating their whole dinners, and what good does cleaning the plate (i.e. making the food gone) do to remedy the situation. :)
> It's a highly rewarding and enlightening process which I highly, highly recommend to anyone that eats meat.
The bottom line of what I'm trying to say is I just can't see anything enlightening, let alone rewarding, in a process which necessitates killing other sentient beings. Of course, there is absolutely no doubt that hunting is infinitely more ethical than what is being done by the meat industry. It's really incomparable, so if you have to eat meat do take care it's from a reasonable source like hunting or “organic” (I hate that word) farming. However, that likely doesn't scale at all at the current levels of population. In my mind the best thing to do would be to just stop killing animals for food.
Some time ago I came across this interesting Youtube video[0] but never got around to post it here, and this discussion reminded me of that[1]. Basically, this guy (a Theravada monk) summarizes almost perfectly what I'm trying to say. Because of the horrible things industrial meat production does, I can't quite agree with him that it's OK to buy meat in the supermarket (as long as you're not specifically desiring meat), but otherwise I think he is spot on.