Compression drivers in horns or waveguides
 

Does the increased sensitivity and max SPL come only from the restricted radiation pattern (e.g. going from full-space to half-space to quarter-space radiation), or is there another mechanism which further boosts the SPL?

Great question. The answer is yes there is another mechanism. When you place a horn on the front of the speaker you increase the radiation impedance seen by the front of the cone. That increases the effeciency (electrical to acoustic power) of the system. Note that the mechanism you pointed out, shoving the power into a smaller area, only increases the pressure in that area and not the total radiated power, hence not the efficiency.

Yes, the efficiency is the ratio of output power to input power, so if input power doesn't change, output power doesn't change either (from the factor you pointed out). Fairly trivial.

How much boost do we get from the transforming of the radiation impedance?

Take a compression driver apart, and you'll see it's constructed a lot like a bandpass subwoofer. There's a driver which fires into a compression driver, and another chamber on the other side of the diaphragm, with a port (aka the throat.)

So there's at least three things increasing the efficiency:

#1 - Compression drivers use a motor which is outrageously large, literally 5x the size of the motor on a conventional tweeter.
#2 - Limiting the bandwidth of the driver increases the efficiency. The response of a compression driver is typically half as wide as a direct radiator (it's a bandpass design after all.)
#3 - The horn or waveguide focuses the acoustic energy into a narrow cone, increasing on-axis efficiency.

#1 and #2 exist regardless of whether there is something in front of the compression driver. I'm looking for stuff more like #3 (and I'd really wish you'd use sensitivity and not efficiency in this context).

That depends on a lot of factors. The driver's parameters, the enclosure the driver is in, and the horn all effect this. It is also frequency dependent. I don't have a rule of thumb or simple example for you and I don't have the time to come up with one right now, but I do have a picture of the basic circuit representation of the system. The key is that increasing the radiation impedance (Zrad in the circuit) increases the ratio of the power dissipated in the acoustic circuit to the power dissipated in the rest of the circuit, hence increases the efficiency.

Mostly all correct

There are three factors that dominate increased "sensitivity"

1) large magnet and Voice coil
2) compression ratio increases actual efficiency
3) waveguide focusing more SPL in forward direction increase sentivitivty, but not efficiency.

How much of each one occurs in dependent on the specific design. There is no one answer.

With a DE250 on an OS waveguide its going to be all three in approximately equal amounts as this combination is designed to optimize sensitivity so everything is done that can be done - very large motor, high compression ratio, narrow coverage angle.

But a direct radiating tweeter on a small wide waveguide is going to gain principly from 3 as there isn't much loading effect and the motor structure hasn't changed.

Any combination of these factors is possible.