Craig,
Sounds like the builder of your cabinets used a lot more fiberglass then I could afford in 1979, or did something similar to what I did.
A 45 foot sailboat generally would have nearly an inch thickness of fiberglass below the waterline, which would make a horn like yours weigh about 150 pounds without an enclosure.
If your cabinets are relatively recent, they could use siped foam core and epoxy (like current surfboards), which was not around in the bad old days. It is very expensive to use those products.
Who is the designer / builder?
Amps delivers more power into a lower impedance, but for a nominal 4 ohm load just set the amp at 2 volts sine wave at 60 HZ, then sweep up. Most meters will be accurate at 60 HZ AC, not so much at other frequencies, so calibrate at 60 HZ.
Lay the cabinet on the side, prop it up paralell to the ground, put the mic on the ground one meter away from the center of the two cones, subtract 6dB for a equivalant LF free space reading.
20 volts at 10 meters would be more accurate, but loud as hell.
As far as excursion, a dot on the cone is pretty easy to see move, but the depth of the horn will make it hard to get off axis enough to measure.
You could gaffer tape a Popsicle stick 4.1 mm from the cone, then slowly advance power and see what voltage is required to make it hit.
The tapping noise should be easy to hear. Start loading the styrofoam “bricks” in the compression chamber and and see what happens.
Without seeing the phase plug design I can’t say what moving the cone away from the plug will do, but for sure the plug should be farther than Xmax from the cone or you are limiting the output.
Don’t expect the cabinets to be flat, there is nothing wrong with EQ.
Art Welter