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Its POI is about 4" down and about 2-1/2" to the right
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You don't mention the distance - this represents a much bigger issue at 7 yards than at 25 yards.
No offense: Chances are that the low-shooting problem is you jerking the trigger/flinching (if you are a southpaw, the right-shooting also). Get someone else who is a known-good pistol shot to shoot the gun slowly and carefully. Get them to do so offhand (not off a rest), and using a couple of ammo brands/bullet weights. If several folks see the same problem with several loads, send the gun back to S&W to be fixed... that's the beauty of buying a factory gun with factory warranty. The fixed factory sights should shoot dead straight, so why spend your own money fixing S&W's mistakes?
The windage correction is easy by drifting the front and/or back sight in the right direction.
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My 40 Pro 5" is 4" low. Solution was to get a shorter sight from Dawson Precision. Call them and they can tell you the correct one. As far as being to the left, I would double check trigger pulling and the rear sight.
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IIRC the Pro sight should shoot to the center of the fiber optic, not the top of the front sight. That may be your issue.