Nice ride! As has been said...gloves, relaxed grip and change hand positions helps with flat bars. Bar ends are very nice because they also get the wrist in a different position too.
Before I got bar ends, I would occasionally switch to having my pinkies and thumbs under the grips and middle 3 fingers on top of the grips (if that makes sense) and that put the pressure on a different area for a while. Whatever you can do to change up the hand positioning along the ride will help.