If that was my boat, I would never take a shower in it. My 28 footer has a "shower" in it that drains (through a line) to the bilge. I hate to think what showering would really do to the woodwork, etc. in the head area. Ugh. I either shower on land or use the cockpit.
I'd remove the hardware (strainer) first, and toss it. Then, set about cleaning out whatever mess might be under there reasonably well. Glassing over the hole would be a pain in the butt, as far as I'm concerned. I'd just use it for a drink holder. Just kidding. But it would go nicely with that backrest you have on your toilet. I'd fashion a cover out of a small thin piece of Starboard material or find a small kitchen cutting board with white plastic that I like, and cut, grind, and drill it into a cover. Then seal with something like 3M 4200, and screw it down to the sole.
So, the sole in the head area, is the liner, which is suspended over the bilge, right? And if that drain hole is right next to your mast (which is on the centerline of the boat), then the drain just empties right into the middle of your forward bilge area. And that area of the bilge, unlike the bilge in your main saloon, has no access cover, meaning it's always going to be kind of skanky in there.
So, water flows into that forward bilge area from the drain (or other sources as yet to be identified), and then flows from that bilge area through the limber holes into the bilge area in the main saloon. Stick a hose in the drain, turn it on, and the entire bilge will fill up, right? Even if you block off the drain hole with a nice cover, when you get some water in your saloon bilge, it's going to travel from there, through the limber holes to the bilge area under the head. The question I would have is, so what? Your's wouldn't be the only boat on the planet with an inaccessible bilge area. Fugetaboutit. Of course, you don't want to plug the limber holes to prevent that, because any water getting into the forward bilge from a leaky hatch, etc., would be trapped in there and be a REAL mess.