I live in Japan. The only time I've used takkyubin for luggage to/from the airport was from NRT or KIX to home (Osaka area). It's never taken more than 24 hours. Check with the ryokan. I'm sure that they will know.

If you want to go to kaiyukan, then maybe you could do Sky Building first, eat lunch, then go there in the afternoon. I think that you take the Osaka Loop line from JR Osaka, then transfer to a subway at Bentencho. I could look it up if someone else doesn't chime in. After that, if there is time left, you could go back into the central part of town via that subway line, for example to Nanba, for dinner, which would be more exciting that the area around the aquarium. Then, catch one of the airport trains or buses to KIX from that location. Quite a bit of walking and train riding, but certainly doable and you'll sleep well on your flight. :-)