They look more like seagulls

I was thinking the same thing. The birds don't look anything like storks. They're just seagulls. I don't know why the animators chose such a design.

"I'm the dude, playing a dude that's disguised as another dude".

I agree, my first thought was albatrosses when I saw it!

Have to agree. The entire time, I was NOT registering "stork" at all.

Yes, nothing like storks.