I LOVE your quilt! I've sketched out a bit of a quilting idea. I would ditch the pieced part of the star, and around the outside of it. I would then quilt a "suggestion" of the pieced pattern into the blank star points, using a wavy line instead of straight. Use your favourite curvy fill for the background (stippling, pebbles, swirls, McTavishing, etc.). The contrast between the straight lines in the pieced part, the almost-straight in the blank points, and the curves in the background will complement the piecing.
I sketched in a "track", showing how the pieced point is being "inserted" into the star. I think this adds an element of motion, but I'm not sure I like it now that I drew it out... I'll let you decide how you feel about that
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I have done a couple quilts where I did most of the quilting on a longarm, then went back and used my walking foot to do straight lines. You could probably do that here to avoid ruler work.