Himeji does not take a full day, in winter it's more a 2-3 hour stop to see the castle.

Don't do Hikone on the last day, it's too much of a detour from the Shinkansen alignment.

If you really want to see "a" castle, I would do Himeji as a half-day trip on Day 4 in place of Umeda (which is just a collection of shopping centers and a giant train station, you'll see plenty of those the rest of your trip), Day 5 Hiroshima/Miyajima as planned, get an early Shinkansen train to Tokyo on Day 6, wrap up any souvenir shopping at Shinagawa on the way to HND.

My nerdy reason for recommending Himeji over Hikone (they're both original constructions about an hour outside Osaka) is that some Nozomi do not call at Himeji, so if you time it right you can really feel the speed of the shinkansen as it zooms past the platform.