I'd recommend against going all the way to KIX and then all the way back into town. You'll kill 2 hours that way. Would also recommend against storing luggage at Shin-Osaka, rather store in the Osaka station area. You can easily get to Umeda Sky Building from there. Also, the kaiyukan is not centrally located, but rather out a bit. It's doable with your schedule, but it's going to take quite of bit of time going back and forth. Underground between the Umeda Sky Building and Westin Hotel next door is a group of restaurants in an area designed to look like a street in old Japan. Nice place for lunch maybe.

Another option is to send your luggage one day ahead directly to KIX by parcel post (takkyubin). Keep only what you need for last day in a shoulder bag and pick up the luggage at KIX at the takkyubin counter.

Edit to add. Rather than taking the shinkansen from Kyoto, you can just take an express train on the regular tracks. Time to Osaka is about 30 minutes.