Not all transmissions are the same... the 700's are long gone! And even those I think got the OD issue fixed (I hope, it was around long enough).
I'd use the manual shift mode, and bump it down prior to a hill. That way it isn't shifting under power. Will it hurt to shift under power? No, it's designed to shift. But I think you'll be happier if you bump it down prior to a climb. On flat ground your wallet will be needlessly drained by towing in drive, so if it will stay in gear, let it go as high as it wants.
Don't forget, these newer 6 speeds run two overdrives. Actually, the GM 6 speed uses a slight underdrive in 4th. If you aren't going past 60 or so, I would give thought to locking out 6th, but otherwise, run it in tow/haul, and perhaps watch ATF temps in the DIC, assuming you can find an appropriate temp rating (no good to watch unless if you know what temp is too hot).