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I know you weren't asking for other ideas in the framing of this shot - but I'll offer one anyway, and explain why I think it would work.
If you "pinned" your subject into the upper left corner, with almost no space above or behind it, the subject - which obviously covers only a small percentage of the frame - takes command of all the space. When this subject floats in the center of the frame, the space competes with the bird for control of the frame.
Why upper left corner instead of lower left? Because you have a strong diagonal component in the upraised wing, and the invisible line from that wing then flows through the frame as well. This gives a more dynamic look.
I haven't taken the liberty of editing your image, and so, having not seen how this placement would work, I can't tell you if it would be the best. But I think you were after the thought process that precedes the composition rather than an analysis of the composition - so that's what I'd try first, for the reasons listed above, and if it didn't work, I'd try something else -