Well, I may be the first to post actual measurements for the question, "Does alternating drivers help", but here goes.
Note, I am measuring a mono-triple in a 1.5" thick MDF H-Frame with normal cavity sizes of 13" x 13" x 6.5" crossed over @ 40Hz with a 48dB/octave slope. No mass loading membranes or open cell foam has been applied to the cavity walls. All measurements were taken without moving the mic located at the listening position and at the same volume and XO settings. At least 9 measurements were taken with all drivers facing forward and at least 9 were taken with the center driver of the triple reversed in a quiet room with no lights, HVAC, fans, etc. running.
For those that are concerned the measurements are being lost in the noise floor, here is a plot (all 3 drivers facing forward) showing THD, the Noise Floor and the first 1-9 harmonics. The noise floor is 15.7dB below the THD plot @ 25Hz and what I have been told from audio engineers, humans are suppose to be able to hear down into the noise floor, but by how much, I don't know. Since there is 15.7dB difference (THD versus Noise Floor) for this experiment, we won't have to go there. Also, harmonics below the noise floor have been greyed out in the plot.

I think there has been 2 lingering questions about alternating drivers, 1) output levels and 2) sound quality (subjective and/or qualitative). Since my hearing is different from everyone else's, I can only share my measured plots and my perceptions of sound preferences.
Reminder: These tests are based on an odd number of drivers so I don't get equal cancellations like folks would who have even number of drivers.
As for #1, output levels, The calibrated mic only sees at most @ a 0.3 dB drop by reversing the center driver. I can get more boost by narrowing the cavity opening or increasing the plate amp's volume level to compensate. From my experiment, with the plate amp's volume level set to 11 O'Clock, I am not concerned with this in-room 0.3dB SPL drop which maybe different elsewhere in the room.

As for #2, sound quality, there is a 2.3dB THD drop @ the 23.3Hz plateau and 4dB THD drop in the peak @ 38.3Hz (40 Hz crossover point, Purple is all facing forward, Blue has center reversed). Can this be heard, I don't know, but I am more than willing to accept this free lowering of the THD. FWIW, the peak at 38.3Hz is primarily comprised of the 2nd order harmonic distortion. The first two relatively unaffected peaks are comprised of odd order harmonics.
CORRECTION: Plot title is incorrect. Should read: "All Forward THD vs Center Reversed THD"

Comparing the multiple measurements, the preceding observations are pretty much consistent throughout. I would expect slightly better improvements using an even number of drivers.
Since we are DIYer's, we should all be interested in how to build/assemble our projects to get the best/cleanest sound possible. Hope this helps giving a quantitative data point on the original question of whether or not to alternate drivers.
Update:
For those concerned about reflections, here is an impulse response of the room and system. GIK Acoustics suggests all early reflections should be down at least 15-20dB within 20ms-40ms.
https://www.gikacoustics.com/unpacking-etc-time-domain-measurements-early-reflections/