Why not try a less central position for the bird, or possibly a panoramic crop?
Apart from going with a different 'arty' crop showing loads of negative space to the left (not convinced it'll work though) there isn't really much eloase you can do with this I'm afraid.
It's perfectly good as a record shot, and the pose is nice, but the large crop and the underexposed subject have put you on the back foot to begin with.
I'm guessing you're working out a way of getting closer!
Because the cuckoo is not tied to any particular nesting site you may find it difficult to tie "him" down as easily as many other species.
How lucky to have golden orioles nearby. I think I may move to France!