Again, the only difference between the multiple plot lines is the delay/time alignments which range from [0ms - 7.25ms].

For this configuration 6.1ms produced the flattest most consistent curve across the 250Hz XO region. It also produced the cleanest step, group delay and frequency SPL plots.

Hope this gives you some ideas if you are inclined to try REW or similar software to see what your rig is doing.

UPDATE: Here are a few more plots showing the delay/timing alignment effects.

Frequency over XO region.

Linear Phase STEP between 0ms and 6.1ms.

Linear Phase IR between 0ms and 6.1ms. Virtually no difference.

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2022/03/30 Historical Records CENSORED

 Vertical Wavelets for Timinng Alignments - emailtim 08:47:17 07/28/20 (1)
 RE: Vertical Wavelets for Timinng Alignments - Barry 10:39:09 07/28/20 (0)
 RE: Phase Matching and Delay/Time Alignment Example Plots - Barry 14:31:36 07/26/20 (4)

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Show full thread outline!

 Vertical Wavelets for Timinng Alignments - emailtim 08:47:17 07/28/20 (1)
 RE: Vertical Wavelets for Timinng Alignments - Barry 10:39:09 07/28/20 (0)
 RE: Phase Matching and Delay/Time Alignment Example Plots - Barry 14:31:36 07/26/20 (4)
 RE: Phase Matching and Delay/Time Alignment Example Plots - emailtim 15:09:49 07/26/20 (3)
 RE: Phase Matching and Delay/Time Alignment Example Plots - shumi 17:39:45 07/26/20 (2)
 RE: Phase Matching and Delay/Time Alignment Example Plots - Barry 10:25:32 07/27/20 (0)
 RE: Phase Matching and Delay/Time Alignment Example Plots - emailtim 19:43:04 07/26/20 (0)
 RE: Phase Matching and Delay/Time Alignment Example Plots - pictureguy 20:36:22 07/25/20 (4)
 RePhase generates FIR filters. - emailtim 22:04:39 07/25/20 (3)
 RE: RePhase generates FIR filters. - pictureguy 00:59:15 07/26/20 (2)
 RE: RePhase generates FIR filters. - emailtim 10:02:50 07/26/20 (1)
 RE: RePhase generates FIR filters. - pictureguy 10:39:28 07/26/20 (0)
 RE: Phase Matching and Delay/Time Alignment Example Plots - BDP24 14:36:34 07/25/20 (2)
 Found this - emailtim 19:43:29 07/28/20 (0)
 RE: Phase Matching and Delay/Time Alignment Example Plots - emailtim 15:43:32 07/25/20 (0)

It is one priority, but not all. The frequency curve seems to be the most common first consideration (e.g. the ubiquitous Graphic EQ and tone controls), but it is certainly not the only one. It was my first focus until I got deeper into it and "learned" better tools.

"... And is achieving that sometimes done at the cost of another criteria? ..."

They are all related so they should all be taken into account. Achieving one goal through improper means can cause other problems.

"... Or does best frequency response usually coincide with best step/group delay response? ..."

Good question. I usually target a flat curve because of my personal hearing preferences. I find that a flat curve is a happy medium for most of the types of music I listen to so most of my experience is with a flat curve. You can have a flat frequency response and still have other issues. Time alignments, phase and frequency will all impact the various plots.

There are also differences between minimum phase and linear phase filters. If you apply a minimum filter to adjust a frequency, it will impact phase. If you use a linear phase filter, it will not. RePhase allows you to select your own combination of minimum and linear phase filters.

There are also linear and minimum phase camps just as there are tube and solid state camps so be forewarned.

In short, minimum phase filters are generally faster, require less processing power and have a higher chance of matching video lip-sync. Linear phase filters require more processor power, have more of a lag and video lip-sync needs to be compensated by a video delay or faster hardware.

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2022/03/30 Historical Records CENSORED

"... rePhase is a free FIR generation tool for building fully linear-phase active crossovers with arbitrary slopes.
It also let you manually compensate for the phase shifts of your loudspeakers and existing crossovers, be it active or passive.
Once generated, the FIR can be applied using any hardware (openDRC, miniSHARC, Najda, ...) or software (foobar, convolver, JRiver, ...), stereo or multi-way convolution engine. ..."

REW supposedly generates 2nd order biquads IIR filters that can be exported in XML format and then imported into RePhase to do frequency correction or you can make them by hand.
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2022/03/30 Historical Records CENSORED

• https://rephase.org/

The 0ms is the green trace heading South West on the PHASE and the green trace second from the bottom of the 250Hz dip on the SPL plot (both just above the bottom/lowest 4ms purple trace).

I should have varied the line styles for added clarity.

"... Are you using RePhase to set the delay times and then using REW to measure all this? ..."

I made all of the linear filters in RePhase.
Exported REW's PEQs as an XML file and imported into RePhase for frequency corrections.
Delays are done in JRMC. You can add delays in the convolution's text *.cfg file or inside either of JRMC's Parametric Equalizers using the "Add Delay" option.
Verification is done with subsequent REW measurements.

"... I'm familiar with the REW group delay plots, but not these. ..."

I did not post any GROUP DELAY plots in the OP.

The multiple-trace plots are created using REW's "OVERLAYS" windows which allow one or more measurements to be plotted on the same graph.

I am using one of the latest beta versions of REW.

I am also using different FDW settings on each plot to emphasize/de-clutter the specific points trying to be presented (i.e. eliminate room reflections).

This is getting a little off topic, but here is the content of the 4 RePhase convolution files which make up the digital XOs, OB/Dipole sub rolloff compensation, phase and frequency corrections. I am using a multi-channel DAC to turn 2-channel stereo into 4-channel stereo which eliminates the downstream passive XO.

Low Pass Convolution files contains:

250Hz Low Pass XO filter
Low Shelf - OB/Dipole rolloff compensation
High Shelf - OB/Dipole rolloff compensation
Sub Phase correction - manual process
Sub Frequency correction - From REW's exported XML file

High Pass Convolution files contain:

250Hz High Pass XO filter
Maggie Phase correction - manual process
Maggie Frequency correction - From REW's exported XML file

Config file channel routing and conv file mapping:

Take input from channel 0 (left), apply convolution file 0 and send to output channel 0 (left high)
Take input from channel 1 (right), apply convolution file 1 and send to output channel 1 (right high)
Take input from channel 0 (left), apply convolution file 2 and send to output channel 6 (left low)
Take input from channel 1 (right), apply convolution file 3 and to send output channel 7 (right low)

Output channels 2, 3, 4 and 5 currently not used, but could be used for tri or quad amping.

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2022/03/30 Historical Records CENSORED

• https://www.avnirvana.com/threads/measuring-with-a-timing-re

• https://www.dagogo.com/legacy-audio-wavelet-review/