The only meat that is strictly off the table is human.
There is a very good reason for "humane" slaughter. Animals that are stressed before slaughter produce terrible quality meat. For example PSE in pork.
Here is an interesting article about it.
I don't buy any of the moral arguments against eating meat I've heard so far. I do think we have a duty of stewerdship to properly care for animals we raise, but I haven't spent a lot of time navel gazing on the issue.
No reason to feel bad for eating meat. Our predecessors (apes on up to us) ate meat.
But hey, if it makes you feel better, might as well skip the steak.