Hopefully further debate will follow on your points of interest as the matters are of importance. However, I also think that you might read up on some basic undergraduate flight mechanics text material as your thoughts are somewhat unconventional and, just possibly, not compatible with conventional engineering assessment.
I should point out that the 4-step recovery procedure I stated was written for an audience of students flying Cessna trainers ...
That's understood. However, the philosophical problem is that what is trained and studied at the start forms the basis of actions in high stress situations later in a pilot's career - especially if subsequent training paradigms are a bit light on, as may be the case in some segments of the Industry. It is preferable, while training to the requirements of specific Types, to make sure that the underlying explanations are not over-simplified to the point of being unhelpful and, perhaps, counterproductive.
movement of the nose away from the ground is not conducive to stall recovery.
Probably preferable to concentrate on the interaction of the aeroplane and the surrounding air flow rather than wherever the ground might be .. other than if ground contact is an imminent risk, we probably can afford not to worry unduly about where the ground might be whilst endeavouring to get the aeroplane back into controlled flight ?
considering a 45 degree bank to the left, applying right rudder would yaw the airplane to the right,
Depends on what degree of control you might have in the particular circumstances. However, presuming that the input produces yaw .. that produces slip and too much slip may precipitate a significant departure. Probably not a good technique as a general consideration ?
which in this case, would raise the nose of the airplane away from the ground
If the former problem occurs, the nose might rapidly point more directly towards the ground. Just what aerodynamic benefit arises from having the nose point away from the ground ?
If you were to use elevator instead - you will point the nose towards the ground,
While that may be an effect, it also will have the primary, and desirable, effect of reducing alpha. How is the ground relevant to the aerodynamic concerns ?
and since the airplane is traveling towards the ground, that will automatically decrease the angle of attack.
That probably will be the consequence. However, one needs to be considerate of the particular Type's pitching moment characteristic - some aeroplanes have nasty spots where the elevator's capability to produce pitching motions is compromised greatly.
Again we should be thinking about the airflow, not the ground. The latter is only of interest were we at risk of hitting it ...
If you're at the critical angle of attack, you can unload the wing by ... increasing angle of attack
Perhaps you can provide further amplification on this suggestion ?
When the airplane is at the stall and there is a wing drop, the longitudinal axis usually gets tilted off the heading in the direction of the roll.
Typical behaviour - further effects of controls stuff from basic training.
By pitching down, while at 45 degrees of bank, you will move the longitudinal axis back towards the initial heading.
And the effect of that might be ?