Based on your observations of spin-down behaviors, sounds like the flat segment might have occurred during sleep. If so, the upward and downward segments could reflect changing tip resistances during behaviors other than sleep.
I believe that the downward segment at the left is mainly due to high air drag.
Then this way "efficiency" is calculated may be misleading because it may lead to believe that there is an increase of the total friction at low speed but this is not true, because we have the lowest total friction at the lowest speeds.
Like James, I too observe continuous changes of the efficiency of the top during the spin.
my tachometer is good enough and I can say that these continuous changes are real.
These continuous and unpredictable changes are due to the tip friction. Air drag too changes, at the decreasing of speed, but gradually, and always in the same way.
Here are the data of the tip friction, (obtained making the top spin in deep vacuum conditions), of 19 spins of my Nr. 27, (156 grams):
the top has an external carbide tip and was spun always vertically so there was nearly no precession at the start of each spin.
The 19 spins are numbered chronologically, the spin Nr. 1 was the first spin performed, when the tip was new and very sharp.
The first two spins are the ones with the lowest friction, telling that a sharp tip has lower friction that a dull tip.
The spins with a red number were performed without lubricant, the ones with green, violet and blue numbers are spins with some different lubricants. It is evident that the tip friction is lower with the lubricants.
There is a continuous and random variability of the tip friction.
There are more important and frequent changes in heavy tops than in light tops, especially without lubricant.
This is the tip friction of a light, (77 grams), top on lubricated spinning surface;
With light tops spinning on a lubricated surface there are not significative up and downs but the tip friction decreases gradually with speed.
I believe that the unpredictable changes of the tip friction are related to wear.
In fact there is wear in the contact points;
this is the photo of a dimple in the carbide spinning surface caused by wear, at the microscope; the dimple is about 0.1 mm large and 0.03 mm deep, and is the result of 50 hours of spinning of a top with a conical tip.
These dimples are responsible for making tops with a recessed tip to wobble spontaneously, (nutate), when they spin on them.