Oh no! I've never dealt with birds specifically (that I know of?) but in general as things get bigger they seem less likely to be totally removed and more likely to just get nibbled on.
I saw another reply (maybe the x post??) suggesting transplanting but I have had mixed luck with transplanting lettuces. Leafy greens do well with covers because they don't need to be pollinated but they are a pain to work under and would need to be propped up later as they grow so I get why it isn't ideal.
Good luck!
