On the step...

I don't know if airliners are routinely assigned a block altitude to climb and descend at their discretion. Without a block altitude, going 100 or 200 feet or more above cruising altitude would be a big problem with ATC. Second, I believe airliners travel much closer to the critical Mach number. Any overspeed in the descent could lead to a dangerous Mach stall.

We don't use block altitudes (well, not typically), although being a hundred feet high won't necessarily cause a problem. There are a number of things that should be cleared up with your understanding of critical mach and how we operate near it, but that's kind of a long response that's better suited for someone less lazy than me. The bottom line is that I could replicate jsstevens' test in my airliner without any trouble.

I'm guessing the reason you don't see it with an airliner is that we usually climb at a speed that is pretty close to what we use for cruise. Before I transition to mach, it's actually the exact same speed. After I transition, it's within about .02 mach, and sometimes even the same if I'm at a lighter weight. Point is, the acceleration that jsstevens is measuring is usually only a few seconds long, if there is one at all.
 
The August Kitplanes magazine discussed measurement of VH ((max level speed at full power) which sounds a lot like getting "on the step"

A level accel starts with the airplane relatively slow (~1.3 VS). With enough power on the airplane to hold altitude, the pilot increases the power to full and focuses on holding altitude as the airplane accelerates out to VH (max level speed at full power). The problem is, VH is by definition asymptotic, and therefore, it takes a long time to get there. Anchoring the point is based on the idea that it is faster to decelerate back into that speed than to accelerate up to it. So when the speed is starting to stabilize, the pilot purposely dives the airplane to overshoot VH, then levels the airplane. At this point, the drag backs the airplane down to VH (faster than if the pilot had just waited for the excess thrust to get him there).
Seguin, E. Back to School There’s always more to learn at the National Test Pilot School (Part 2). Kitplanes August 2015, p 24-30

It seems "getting on the step" is simply just a way to get to the VH a bit faster; as an asymptotic function, it may be a lot faster way to reach the maximum speed.
 
The August Kitplanes magazine discussed measurement of VH ((max level speed at full power) which sounds a lot like getting "on the step"

Seguin, E. Back to School There’s always more to learn at the National Test Pilot School (Part 2). Kitplanes August 2015, p 24-30

It seems "getting on the step" is simply just a way to get to the VH a bit faster; as an asymptotic function, it may be a lot faster way to reach the maximum speed.
Yep, I actually suspect this nails it.
 
So, the step is a farce however I have noticed a similar phenomenon when pulling my trailer on the highway. Goes like this:

When driving level, I get about 11mpg at 70mph. When climbing a hill, I get about 4.5mpg at same speed. Going down the other side of the hill, I get about 30mpg at same speed. Then, when level again, I get about 15mpg, level, at 70mph.

Can't explain that one.

OT, but same RPM? If not, and it's an automatic, your torque converter isn't locking up fully in level pull and then is, once you go down the hill on the other side at lower power. Very hard on the transmission and will build a lot of heat fast.

If same RPM, the mpg gauge is lying.
 
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