When I ride my flat bar road bike (Jamis Coda) I generally keep my hands just like you describe. If your hands are getting sore it's likely that you are putting too much pressure on your hands. As you improve your core strength you should get better in supporting your upper body from your core rather than from your arms and hands. Give it time.
Are you wearing bike gloves?
I like the Titec Hellbent grips



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