I'm not as familiar with poolside showers or changing options. But many of the DVC resorts do offer that (I'm familiar with very nice options at OKW, AKL, and BC, so I expect SSR has them, too). You should have access to SSR the entire day of your check-out and should be able to store bags (if needed)
, enter/park, and shower/change by the pool. Late check-outs for DVC rooms are very few and far between, and those that get them might get noon or perhaps 1PM at the latest. Doesn't sound like that would help you. Sometimes folks in your situation rent an extra night on the room to give them later access, but not sure that's an option for you.