That is beautiful! If it is wool then you might want to try reblocking it smaller.
If you opt for the elastic, I would tend to put it through the stockinette sections above each set of ribbing because the weight of the ribbed part would tend to overstretch thinner elastic thread.
Another fun option might be to play with adding two I-cord ties midway across each shoulder. You could tie them, or just the added weight dangling might keep the shrug up higher on your shoulders.