Yea, killing hawks is illegal. So just tell us you're killing the brown crow.
I am so sorry.
You can get cotton knotted netting that's really strong and cover their yard. 10,000 sq ft is about 100'x 100'? A lot of room but they make the netting for large areas like that. It'd probably be a few hundred dollars but it sounds like your priorities are in the right place and you wouldn't have a problem putting the money where your birds are (so to speak).