Sounds like continuous curves would work for you. Those are stitched kind of like the traditional straight lines a quarter inch all around inside a piece, but are curves instead of straight lines, with the ends stopping at the intersections. The curve just bumps into and right out of the intersection to make the next curve. If you experiment with paper and pencil (or dry erase marker on clear vinyl overtop a sketch of the piecing), you can work out the best route to machine quilt the continuous curves to minimize stops and starts.