In my last fort, I separated the dining hall and food stockpiles from the rest of the fort. The only way to enter or leave was through ten hallways that looked like this:
with the door to the left being pet-impassable. Whenever I noticed a pet between the doors, I locked both of the doors and ordered the lever operating the hatch to be pulled, which dropped the pets into 1x1 holes.
AFATWK*, a pet in a 1x1 area doesn't slow down the simulation much because it's completely immobile.
Anyway, sometime later in the game I flooded all the holes with magma. None of the dwarves got upset. Yay for boozecooking and legendary dining rooms. The pet-massacring, vomit-inducing, carelessly-smashing-dwarves-under-the-automatic-drawbridges monster that I am didn't get any real tantrum spirals. hah. (It also helps that all dwarves that actually went berserk died within 20 frames.)
*As Far As The Wiki Knew