there aren't any times that the bird sounds are alone to capture just that noise.
Even if there were, Noise Removal isn't for "Anything I Don't Like." It works best on constant, unwavering sounds like fan noises or air conditioning rumble. It's terrible on noises that constantly change like bird chirping.
The Profile step sounds elegant, but all it's doing is creating a series of sharp filters that take out the target sound and overtones/harmonics. It also takes out those same sounds that happen to be common to other parts of the performance. That's why people instantly complain about aggressive noise removal turning human voices into bubbly garbage. Many people counting on turning their noisy office into Glen Glenn Sound Studios with a simple filter have to return to the drawing board.
And so do you.
We can't split apart a mixed recording into individual instruments, voices, effects... and birds. I would guess trying to manually filter the bird sounds would trash the surf wash sounds.
I enjoyed the mix of sounds. Those bird types wouldn't be caught dead at the beach. Somebody had a good time ad-lib mixing sound types without regard to nature.
You should contact the author and see if they would be willing to create a custom version for you.
Koz