Consider doing Hiroshima and Miyajima as a day trip on your last day. We took the 7:20am non-stop from Kyoto station, left our luggage at Hiroshima station, spent the early part of the day hiking on the island and the afternoon walking around the peace park and the museum. This eliminated a check-in/out cycle, and the day didn't feel too rushed even though we were leaving.

Granted, we flew out of HIJ instead of KIX, but you could catch a 5:15 Shinkansen from Hiroshima and be at Kansai by 8:00.