Well Phil,
I think a guy could easily do carry-on only for the PG. Especially since country-club casual means you don't really have to bring a sports jacket, let alone a suit.
But, if you're travelling with a lady, it might be hard for her. I don't like dressing up, but I did have my wrap skirts, and nice blouses, and summer dress, and three pairs of sandals, and...you get the picture. I packed all my husband's nice shirts in my suit bag along with most of my duds, and then we both carried a carry-on.
But the point is, if one of you has to check a bag, then you've blown the reason to try to skimp--you might as well bring along a few more changes of clothing, or an extra pair of shoes.