A second alternative, although it sounds counter intuitive:

Reverse your trip. Get the 2 day Kansai Area Pass at KIX and immediately use it on the Haruka all the way to Kyoto. Drop bags at your hotel and use the Pass to go to Nara and on to Horyuji. The Haruka is fast enough that you won't really lose all that much time over your proposed route and your bags will be where you want them. The route from Kyoto to Nara is far simpler than KIX to Horyuji on local trains. I really did not enjoy the little commuter train from Tennoji to Nara.