We buy 2 sides of beef a year for $4.59/lb - that's what I pay for the packages of meat I drive away with and put in my deep freeze. I'm in Canada. Honestly, in every town I've lived in, it's been by word of mouth that I've been able to find a good source for grass fed beef. I've also been able to arrange making 3 post dates cheques over three months because I've helped the farmer get new customers through my connections in the homeschool community and other groups I'm involved in. Because of this, they have also been holding my price the same for the last three years.
Another thought is that you could look up suppliers who sell to health food stores? Farmers markets? They might sell for cheaper without the middle man. The farmer I buy from sells their excess beef at auction every fall, so that could be another route?
Good luck with this! The fall comes upon me fast every year so I need to remember to put aside a little grocery $$ every month for this significant expense. My last cow was 400lb of meat!
ETA: We got a pig once but I didn't enjoy the meat cuts - verrrry fatty.