Hmmm. I see what you mean. The wrong side is facing, and you have to pick up stitches. What if you flipped your work up so that you can see the right side. Then you can hold the edge with your left hand and pick up stitches through the top.
Another way would be to pick up stitches with a dpn from the top and then slip them to your main needle.
Or you can bring the tip of your needle to the back of the piece and pick up stitches purlwise. Keep the yarn in the front, and bring the needle through the back and pick them up as if you were purling.