Yes, correction of individual drivers is totally the way to go. This give best quasi anechoic response.
Then when the speaker is placed in whatever room, global correction of the entire system is OK. But global correction for the speaker itself is very sub optimal ime. Best to tune speaker first, then adjust to room.
Pls see my reply to dasdoing re pre-ring.
If you are wanting to use FIR around 130Hz, a very few taps will not work. The frequency resolution will be so low as to be totally ineffective.
Look at the slippage in rePhase down low when you try to reduce to a few taps.
It looks like its just a timing difference causing the glitch in the spectro at about 180Hz....like the speaker needs a little more simple delay relative to the sub.
Here's a spectro of a 4-way i made indoors that shows both good point and bad points as they apply to this thread.
Note the smooth integration between sub and main at 100Hz. This was made with 96 dB/oct linear phase LR xovers at 100Hz, 650 Hz, and 6.3kHz. Non of those xovers produce any pre-ring, as complementary linear phase xovers cancel pre-ring.
View attachment 190562
However, this spectro has phase flattening, and insufficient taps to flatten mag, on the very bottom end of the sub's roll-off.
Here's the mag and phase trace that goes with the spectro.
Note how phase stays flat below 40Hz, whereas mag (SPL) is rolling off.
A linear phase high-pass was used for the sub......and that will cause pre-ring, because there is no complementary off-set.
The HPF should have been minimum phase.
Hope this all made sense....
Bottom line is, sub to main integration is very doable....but best if done outdoors co-located, (stacked together etc) before being brought into room.
View attachment 190563