Hi, Yes, you can use JR all the way. You'd need to start at Hamamatsucho Station, and then go to Shinagawa to catch the bullet train to Shin-Osaka. From there you can get the Haruka Ltd Express to KIX or use another train, depending on your timing. One example is here: https://bit.ly/2Gyet4j Just change the date/time to what you want.
I might go back to JR Tokyo station for a relaxed boarding to a bullet train. At Shinagawa, bullet trains should not stop at for a long time. The train might begin to leave the Shinagawa station before you sit on your seat.
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Yes, you can use JR all the way. You'd need to start at Hamamatsucho Station, and then go to Shinagawa to catch the bullet train to Shin-Osaka.
From there you can get the Haruka Ltd Express to KIX or use another train, depending on your timing. One example is here:
https://bit.ly/2Gyet4j
Just change the date/time to what you want.
I usually use Google Maps to find the nearest JR stations and check the results with the Japan Rail Pass tool below. The route via Tokyo is listed as Route 2 in the following.
https://www.google.co.jp/maps/dir/Tokyo+Shiba+park+hotel/Kansai+International+airport/
https://world.jorudan.co.jp/mln/en/japan-rail-pass/?p=0&xpd=1&from=Hamamatsucho&to=Kansai-Airport&date=04/18/2018&time=09:00&ft=0&sub_lang=nosub