What is the methodology to select the LP frequency for the different subs, assuming one has access to high resolution acoustic measurement equipment?
Basically you feed the subs with an identical signal derived as the sum of all the channels (LP'd or not, but if LP'd then do it above 150 Hz.). Most receivers send out such a signal as LFE, as an option. If not, then you must do this somehow. My receiver does so I have not had the need to do anything different.
Take this signal into all the subs if active, or preferably a DCX2496 which then drives N rack amps (or N/2 if stereo amps), where N is the number of subs. The DCX can do up to three subs, more than that requires a second DCX. I prefer rack amps as I have had endless problems with plate amps.
I start by measureing the mains, then add the nearest sub, which will tend to end up the one with the most output. Adjust the sub for best "mix" with the mains as a spatial average. Now add in the next closest sub. You will likely have to tweek the existing subs setting for the best sum of the two subs and the mains. Keep adding subs as desired/required. In general, each new sub should have less output than the previous one. If not, then I suspect that something is not right since each new sub should only be a smaller correction to the existing result.
If it sounds like this is not a precise formula, then that is correct - there is no precise formula that works every time, just as there are no two rooms that act the same at LFs. So each process and result is unique. Thats just the way it is.