High output coincidental / quasi coax 3 way speaker concept

I think You can time-align Your drivers by using different order filters, but this demands Your drivers are pretty flat both for FR and impedance, and without any steep/abrupt phase changes for at least an octave above/below xo freq.

For passive filters, at xo, a 1st order filter will be 45deg delayed, a 2nd order 90deg, 3rd order 135deg and so on. In general, order x 45deg = phase at xo.
By proper choice of filter order, You should be able to compensate for the physical lenghtwise (z) distance between the drivers' acoustic center.

E.g. xo=500Hz, MF->LF=0.172m, then 360deg*0.172m/(344/500Hz)=90deg => You need 90deg extra phase for the driver to be delayed, which translates to use a filter with order (LF-filter-order +2) for the MF. Use filters with Q=0.5 if possible, they sum up flat at xo.
For vertical directivity of line arrays You should check out Horbach-Keele -filters.
 
and only if the crossover frequencies are incorrectly chosen.
Sure, so there is no real issue here?

In deciding this, if the factor that is constraining the range of possible choices happens to be lobing and the effect of separation if you cross too high, then the plane of the lobing could be seen as tilted to the side (presuming this is a top down view). The assumption that there would be no delay under these conditions might see the listening position under a null.

Measurement will clear this up.

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If we do not take into account the phase rotation by the passive crossover filter. Then the acoustic center of the HF speaker and the midrange speaker in this configuration can be matched only by introducing a delay line into the HF band, since the HF speaker is closer to you than the LF speaker. But with passive filtering, the crossover filter itself will introduce a time mismatch that will not allow you to match the acoustic centers of the speakers using a HF signal delay. Simply put, if you want to match the midrange and HF bands in time, you need a DSP that can introduce a delay into the band and make a phase-linear digital crossover.

I agree with this the LF acoustic centers are too far back for time alignment with HF; passive XO would also introduce additional phase offset and non-linearity (especially if higher order) to make coherence nearly impossible.

@profiguy you might pick off some ideas from the myriad coherent minimalist experiments I've posted to the Fullrange Photo Gallery. If your baffle configuration is more like LF/HF\LF i.e. "symmetric-MTM LX flipped on its side" (maybe this is what you intended?) then the acoustic centers can be physically lined up to time-align on-axis (think LX); the XO phase-alignment would require a bit of design/tweak. You might also consider a MEH-like tapped LF arrangement without the horn (see Minmeh vs T/MM vs TM coherent minimalist).

My M.O. for precise time-alignment has been described in various threads e.g. recent Dunlavy.