I like your border idea with the little pinwheel blocks. The solid strips would frame the center and "contain" it. Great quilt!
I definitely prefer the pinwheels, as they "echo" the main block.
Added: Depending on how many little pinwheel blocks you have, they wouldn't necessarily have to be spread out equally all around the edge. Perhaps just an equal number centered on each edge, or grouped around each corner.
Oops! Didn't see you were thinking of white for the border. My preference is for black.