OK, I've given this a little further thought.
The ST324 as described in the Climax article is pretty much limited to the 3.15kHz high-pass function. This is not too far from the 5kHz stock crossover. Not having measurements of the midwoofer array suggests that an experimental approach would be the most practical. Here is my suggested approach:
1) Start with installing the ST324, retaining the woofer crossover inductor (0.36mH) and replacing the original 1.5uF capacitor with a 0.62uF value. Listen to the system with a focus on whether the treble is too loud or too quiet.
2) If the treble is too loud, try a smaller cap; if too quiet try a larger one. Repeat until it seems balanced.
3) Then try reversing the phase of the tweeter. Choose the phasing that sounds fullest in the low treble/high midrange, i.e. around the crossover point. You may want to re-visit the cap value for best balance if you changed the phasing.
4) At this point, it may be good enough. There are two possible ways it might be less satisfactory - the woofer array may still have enough output above the crossover frequency to muddy up the treble; and/or the small 11kHz resonance in the tweeter may bee too aggressive. Choose the most annoying issue first.
- To restrict the woofer treble, add a capacitor across the woofer array. Start with 3.3uF and increase the capacitance in small increments to find the best-sounding value. With each change, try both polarities of the tweeter, since the capacitor will alter the phase response.
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-to kill the 11kHx resonance, install the Climax notch filter across the tweeter (that's the series 5.6 ohm/0.82uF/0.25mH network).
5) The tweeter tweaks described in the Climax document are optional, and can be done at any time - they won't have a large impact on the crossover design, though we found them to audibly improve the sound.
That should get you about as far as is practical.