I would use frozen spinach, thawed then drained and pressed so all the moisture is out and chopped finely. It would eliminate the need to cook it.

Also, if you are feeling adventurous, and you like it, grill and the finely chop some fennel bulbs and add it in a very thin layer. You could possibly even combine it in the layer with the meat which may be the best option if you decide to use it. It would give it a zing.