You could just leave it open and put a couple of lifelines across it. If your cockpit got swamped you would drain much more rapidly with that "open transom". I don't think the board installed would be a structural requirement since your backstay is split and way out at the corners of the hull/transom. If you wanted to enclose the transom I think a big piece of starboard with a drain slot in the bottom would work fine.
I have seen at least one other N28 with this transom cutout. I think it was a factory option for easy climb in access (prior to sugar-scoop transoms).