If you're gonna wash it at all, I would turn the edges, when using a straight stitch. However . . . (thinking outside the box, here) you could kinda cheat a bit, by using narrow ribbon, for your vines. As for the buds and leaves, you could use that method, where you sew fusible interfacing to the right side, then turn it. Turning with the interfacing turns the edges, for you. I believe there was a tute on the board about this, not long ago.
The quilt is gorgeous!