Hw45 poi higher at lower power

This is typical in handguns. A slower projectile will be exiting the bore as the gun has risen more in recoil. before the projectile has exited the muzzle. This is particularly prevalent in Magnum PB Handguns. Switching from a .44 mag load to a .44 special, or a .357 to a much slower .38 will show exactly this. As you already know, handguns recoil upward much more than a long gun. This makes the phenomenon particularly noticeable. In long guns, particularly heavy bench guns, the effect is often times exactly the opposite, or barely noticeable. 

It is a bit confusing to new handgun shooters as it is exactly the opposite to what most have learned to expect. However at lng ranged, the balance it tipped in the opposite direction with the slower pill. ;<)

KnifeMaker
 
I suspect that the pellet spends a little more (not much but not negligible) time in the barrel. As the pistol recoils the exit time changes the position of the muzzle just a bit higher and the poi is higher as a consequence.

Exactly correct. Pellet speed has nothing to do with it - this wierd close-range behavior is all about the recoil characteristics of this gun.

When you first release the trigger, the spring pushes the piston backwards, and its equal-and-opposite reaction pushes the muzzle of the gun forward. Since the gun sits above your hand, this rocks the muzzle downward. Milliseconds later, the piston stops, pushing the gun backwards, and the muzzle upward. This all happens so fast, you only notice the latter action, but the pellet actually exits during the instant the muzzle is down.

(This is why the rear sight on these "backwards" pistol designs is significantly higher above the bore, than the front sight - you're actually aiming high to compensate for the muzzle being down.)

On the P1's low power setting, the muzzle isn't pushed down as far, so the pellet follows a higher trajectory than on high power. I figured this out years ago, right after I got my P1...and found my first low-power shots stuck in the wall above my pellet trap!
 
I don't know about air pistols, but this ISN'T the case for powder fired weapons as suggested above.

If you've seen any shooting in very slow motion, the barrel movement is neglidgeable to none, before the bullet leaves the barrel. 

First a puff of air, then the bullet, then a little rise, then the slide (semi-auto) hits the frame stop, that's when the majority of the recoil rise takes place. The recoil starts well after the bullet is out of the barrel, and the main rise in hand position is when the slide hits the stop in the frame.

The recoil movement is probably much quicker on revolvers since there is no moving parts to soak up / slow down any recoil.

I'll try my P1 and see what I feel / see target wise. Should be interesting to see per the above info.

Mike