John,
The problem with the linked Speaker Directivity modifier is it does little in the frequency range where the 15" beaming is a problem, above 800 to 1500 Hz or so.
Above 2K it is effective, but also reduces overall level by around 10 dB, the "highs" will only sound half as loud, and would require 10 times the power to be at the level they were before attenuation.
A simple solution to widen dispersion is to reduce the width of the speaker opening to around the wavelength of the upper range that you want to be -6 dB at 45 degree off axis.
Below is a picture of a dual 10" using this technique, I played with the opening width until the 10" matched the HF horn at the acoustical crossover point of 1500 Hz.
Another advantage of covering the sides of the speaker is it creates an acoustical high pass filter, getting rid of some of the problems Bennett mentions in point #3 in post #3. In the case of the dual 10", the crossover was much simpler because cone breakup above 2K was acoustically reduced in level.
As a side, the 2x10" has been reduced to a single 10" in large part because of what he mentioned in point #2 in post #3, and how difficult it is to make a good passive 2.5 way crossover that does not exhibit the problems Bennett mentions in post #5.
That said, there are passive 2.5 way implementations that work quite well, the UREI 2x15" with a coax top speaker comes to mind.
Art