This is how the unbalanced top moves;
the top tends to spin about its center of mass, which is shifted from the geometrical axis of the top because of the added weight on a side of the flywheel.
Because of inertia, the center of mass tends not to wobble, and tends to make its spiral trajectory without waving.
The tip too would want not to wave, driven by the spinning surface.
But since the ball tip and the center of mass are not on the same axis, at least one of the two is constrained to spin around the other one.
At high speed inertia wins and the tip is constrained to wobble, slipping on the glass surface and tracing the waves.
At low speed the friction of the tip wins and it is the center of mass that wobbles, while the tip tends to trace a linear track, without waves.
https://www.youtube.com/watch?v=1yomsrBnf-cAt high speed there is also back and forth slipping of the tip along the precession trajectory.
The center of mass, and the spin axis of the top, which passes through it, in fact tends to move at constant speed, (the equidistant vertical dotted lines in the drawing below).
The traslational speed of the off centered tip instead is variable;
it is faster between B and D and slower between D and F.
So the tip slips braking the precession between B and D, and slips between D and F accelerating the precession.
There is a rapid sequence of alternate braking and accelerations.
The resultant traslational speed of the tip could be not a simple average of the maximum and minimum speeds;
the center of mass, because of the off centered tip and the tilted position of the top, goes up and down, while the top spins.
I projected the center of mass, (orange dots), on the plane of the contact line of the ball, (yellow dotted line);
the center of mass is accelerated upwards between B and D, and downwards between D and F.
With enough speed and sufficient off centering of the tip, the top could even jump and stay in mid air between D and F.
In my test the track was continuous, so the top didn't jump, but, in any case, its apparent weight is lower between D and F, and higher between B and D;
consequently, the top has more grip between B and D, and slips more easily between D and F instead.
So, the braking phases are more efficient than the acceleration phases.
For this reason, the top goes at a lower traslational speed than expected.
This seems to me a plausible explanation of the increased percentage of "positive" slipping in the unbalanced top, (15 instead of 10%).
I am not sure that positive slipping is the most correct term here, because this extra "positive" slipping does not produce a traslational acceleration of the top, nor rising torque, (in fact in my tests, unbalanced tops do not rise faster than balanced tops).
Side view of the ball tip of a top spinning. The top is spinning counterclockwise, and going towards the right.
The yellow dotted line is the contact line of the ball, its upper part is towards you, its lower part is towards the inside of the screen.