I'm not a vegetarian, it would be quite hypocritical for me to invest resources in saving one bird for "care" reasons and then going to eat a chicken at dinner.

This strikes me as backward reasoning - if your moral intuitions about large numbers of animals dying are broken, isn't it much more likely that you made a mistake about vegetarianism?

(Also, three dollars isn't that high a value to place on something. I can definitely believe you get more than $3 worth of utility from eating a chicken. Heck, the chicken probably cost a good bit more than $3.)