From our experiments on our C Dory 25, near the same vintage; the floor was finished with rolled out thickened gel coat. If you don't put gel coat against a perfect smooth and waxed surface, it will not be smooth and glossy. If you roll or paint it on, it will have to be sanded, then compounded to achieve a gloss, or you can cover it with something like Saran warp, or coat with PVA.
The cockpit of the 25 has the same finsih as the floor of the cabin (or as you call it the bilge). When we re-did the cockpit floor, we took white gel coat, added a very small amount of black and thickened it with Cabosil (fumed silica) to the consistance that it would "stand up" when rolled. If you want to "refinish", use waxed white gel coat, add a couple of drops of black, and a high quality, roller (which will not loose nap, or come apart with the polyester resin) and roll that over the existing clean floor. I would sand off the "Peaks" of the sole, since it is too agressive. Then after washing with soap and water, and a scrub brush, let it dry well, and then roll on the new finish.
You can also use any deck paint, but with the agressive finish, I suspect that most paints will not wear well.