Yes, barrel harmonics does whip the barrel around in all directions, but on rifles it doesn't make it go upward (or rather, the amount of climb due to recoil is miniscule compared to barrel harmonics)

Any change in bullet velocity can cause the harmonics to change, and the bullet to leave the muzzle while the barrel is swaying in a different direction. But again, this is in any direction. not just upward. (unless you have a very bad stock that puts tension on the underside of the barrel, causing the harmonics to be primarily upward.. but then you'd see a lot of inconsistency in all your shots, since the stock would be a factor with variables)

You are correct that lighter bullets have less impact on harmonics and the amount that the gun recoils while the bullet is still traveling through the barrel. (which is what makes a 5.56mm very forgiving in terms of poor shooting stances, where as a 7.62 will punish any shooter mistakes).

However, it is not correct that a low velocity bullet will shoot higher because the bullet is longer time in the barrel, allowing the gun to recoil further before it leaves the barrel.

If the bullet weight is the same, the gun will recoil the same amount during the bullets acceleration.

Lets say a bullet is in the barrel for 1/1000th of a second, and the bullet to gun ration causes the gun to recoil backward by 0.05" while the bullet travels through the barrel. that means the gun recoils backward at 0.05" per 1/1000th of a second. If we now decrease the bullet velocity (keeping the bullet weight) so that the bullet will stay in the barrel for 1/500th of a second. This means the gun will recoil 0.05" in 1/500th of a second.

Changing the bullet velocity will not change how much the gun moves while the bullet is in the barrel, it will just change how fast it does it.

On pistols the recoil does cause the bore axis to start climbing while the bullet is traveling through the barrel. But again, this climb is a factor of the bullet weight, not it's velocity, since as mentioned above. the gun will recoil the same distance, but in a different time frame.

Lighter bullets will have less muzzle flip in pistols than heavy bullets, causing the bore axis to be lower at the time the bullet leaves the barrel.

Obviously, all of this is just about the internal ballistics. Once the bullet leaves the barrel, the low velocity bullet will have a more curved trajectory than a high velocity bullet.