An alternate way to save space is to use via-in-pad. If you aren't doing that already, it might save you enough space you won't need one of your two blind via types.
This was meant to be a flippant comment, since it technically answers the question, but doesn't really provide any new information. But the OP seems to think it's useful:
Q: Is there any way to route a signal from one side of the board to the
other without at least one set of microvias?
A: Yes, use a through via.
This is my understanding, based on very little knowledge:
The the return current for the high speed part of the signal will take the path of least inductance. This means travelling along whichever plane is closest to the track. (In fact, it will travel on the side of that plane closest to the track).
When your signal track moves from the top layer to the bottom layer, the return current will want to move from one plane to the other (whichever is closest to the track). If these were both ground planes, then your second image would be fine. You can simply connect the two planes together with a via. But in your third image, you can't connect the two planes together with a via, because this is a short circuit.
If only there was some way to allow the high speed part of the return current to move from one plane to the other, without shorting out those planes. If only there was a component which conducted high speed signals, but blocked DC current.
Oh wait, there is. It's a capacitor!
The return current will flow along one plane, then, when the signal track changes layer, the return current will come up one via, through the capacitor, down the other via, into the other plane, and continue following the track.
In fact, this is exactly what the diagram shows in the yellow arrows.
Best Answer
Vias have inductance and the more spindly they are, the larger the inductance. Note that in the equation above, inductance is proportional to the height of the via multiplied by the formula in the square brackets. That square bracket formula result is smaller when dimension \$d\$ is larger hence, inductance drops with larger diameter vias.
Picture from this website.
You also can't rule out parallel resonance with its parasitic capacitance either. The inductance and capacitance of the via form a parallel tuned circuit and, that could block a high frequency component of a signal in some cases. Using two different via sizes side-by-side might be the way the designer had in mind of "spoiling" the resonances.