The fact that fewer birds from each replicate will be used for sampling leaving more than half from each experiment unused is the problem, which in effect is related to cost.
It depends completely on what you are measuring and what your treatments represent. Are the birds in an individual pasture all receiving the same experimental treatment? If so, then pasture is the observation unit, not the bird. You can create smaller pasture sizes and have multiple pastures getting one of N treatments. In this case, the average response for birds in the same pasture is the mean for that pasture.