Stopping down in terms of going to a smaller aperture like F11 or more...?
I think you mean an f/2.8 or so...and looking at the bokeh afterwards?
I doubt if the reflection should have had the necessary sharpness (not being in the DOF)in this case.
Interesting issue though...
I think I already posted some images with a big opening f/4 or so recently...but you are right if you had in mind a relatively small bird's bokeh with a big aperture as the images posted were rather mammals or similar sized animals....
Green Sandpiper (38)