Now when you say 1/2 ply from the outside you are talking about the floor and your loft can be shut up tight at night time and no drafts and the baby has some nesting material and maybe a nesting bowl?? c.hert
You can still provide nesting materials, they might take them to reinforce the nest. Also, if possible, add one more layer of plywood (similar thickness), lift up the current plywood without disturbing the nest, slide in the nest layer and replace the plywood with nest back on top of it.
Do it only if you are confident that the parents would not abandon the current nest. As long as one of parents are sitting on them, they will be quite ok.