I'm going to attack this from a more general point of view. Your broad question is "should I use a longer stride with less frequency, or a shorter one with more frequency?"
Roughly speaking, as speed goes up -think slow walk to faster and faster- we go from relying on frequency, then we quickly transition to longer strides, then we go back to using more frequency and more more length.
Another way to view it:
- Slow walk => short strides
- Faster walk => strides get longer
- Jog => frequency picks up / strides get even longer
That's a rough idea of what the average human does. When I was in college, it was then presumed humans had it optimized. That is, so many fall into that pattern, and humans are so good at minimizing metabolic cost, that's probably the best way to approach it.
For instance, if you want to go from slow walk to fast walk, you should probably rely on stride length, not frequency. In other words, do what's natural, opposed to trying to outthink nature.
I realize this may not be as precise as you want, but the moment you try to get more precise than this you will run into trouble.
Reason being you are going to be extremely hard pressed to find any hard rules about what's optimal for you, and you will easily find exceptions to any "rule."
We don't even have hard rules for elite performance.
For a long time it was assumed 100 meter sprinters could not be too tall. The thinking was their height made it take them too long to get going in the early stages of the race. Their stride frequency just couldn't be high enough to compete with shorter sprinters. The average 100 meter world record holder was remarkably steadily around 6 foot, give or take an inch or two.
Then came Asafa Powell at 6'3".
And then came Usain Bolt at 6'5".
Bolt, a guy whose stride looks like this. (He has a big shoulder lean to the right, because he has scoliosis!)
Michael Johnson long held the world record in the 400 meters. He had a bizarre looking stride. He was huge on stride frequency.
Two of the fastest people ever; two very different gaits.
Whether you're tall or short, have long legs relative to your torso, have achilles tendons which have a better stretch reflex or not, whether you're in-shape enough to go two steps at a time or whether it will quickly burn you out, these are all going to factor in to what works best for you when e.g. climbing stairs.
No way to find out except experiment.