That's very pretty. I would probably go with a cross hatch in the rest. Lots of stops & starts to go around the pinwheels unfortunately, but I think it will look really nice. You might want a large cross hatch, just to give you more space to deal with some of the challenges - you should be able to ease the fabric and get any "puddles" to end up between the cross hatches without actually pleating the fabric as you quilt, if you are careful.
For future reference, I think you might have had more luck if you had done the cross hatching before the pinwheels. I normally try to quilt center out, and do the larger areas first to stabilize the quilt.