I hope these measurements are useful information to people interested in the topic of amplifier/speaker matching.
First let me describe my test set-up. I made all measurements using LinearX's LMS version 4. The "wooferbox" is a 2.5 cubic foot test box tuned to 35 Hz, with a 12" prosound woofer in it. I placed the wooferbox on the floor away from walls (that was convenient), and placed the microphone about 12 feet away and close to a corner (that was also convenient, and some corner reinforcement would make sure the data was well above the noise floor). I did not use time-gating.
The room is my basement, and it's not ideal but hey it's paid for. My goal was not to get nice pretty ad-copy-quality curves, but to be able to look for differences by comparing the curves. Once the measurements began, I did not touch either the microphone or the wooferbox.
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Here's the impedance curve:

You can see the tall twin bass impedance peaks, and the inductive rise at high frequencies. Also, looks like there's a resonance at 230 Hz. That's not predicted by the internal dimensions, so I don't know what it is - but it doesn't matter for our purposes.
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Here we have the measured frequency response curves of the wooferbox driven by a high quality solid state amp and by a high quality OTL tube amp. I matched up their levels in the region where the impedance is roughly 8 ohms, so it's easy to see the differences:

The red trace is the solid state amp, and the blue trace is the OTL tube amp (no political implications intended). Room effects dominate below 200 Hz - in the real world, this is no surprise. Anyway as you can see, below 100 Hz the OTL amp is generally about 3 or 4 dB up, with the biggest differences (over 6 dB around 25 Hz and 55 Hz) corresponding with the peaks on the impedance curve (scroll up a bit and you'll see). From 100 Hz to 600 Hz the two curves are quite close together, though you can see that between 125 Hz and 250 Hz the solid state amp is up a bit due to the impedance dip in this region. Finally above 600 Hz the curves diverge once again, as the OTL amp puts out increased power into the high impedance presented by the voice coil's inductive rise.
Just eyeballing these curves, I think you can see that the tonal balance would differ depending on which amp is used. Of course adding a tweeter would make more of a difference than careful amplifier choice!
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I recall that the OTL amp's output impedance is in the 7 ohm ballpark, so I went back to the solid state amp and wired a 7 ohm resistor in series between the amp and the speaker. I increased the gain so that the measurements came out very close to one another in the region where the speaker's impedance is around 8 ohms, as this makes it easier to see the differences:

The red trace is the solid state amp direct, and the green trace is the solid state amp + 7 ohms. As you can see, adding 7 ohms of series resistance produces change identical in pattern to what we saw when comparing to the OTL amp. Steve Eddy, you were right! I WAS making things much more complicated than they really are.
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Before we go, let's compare the OTL amp with the solid state amp + 7 ohms series resistance:

The blue trace is the OTL amp and the green trace is the solid state amp + 7 ohms. It looks like the actual output impedance of the OTL amp may be a bit higher than 7 ohms.
I hope this shows why amplifier-to-speaker matching can make a difference if you're looking at specialty tube amps. In particular, I hope it shows why the bass response of some speakers may either benefit from, or be degraded by, an amplifier with a high output impedance.
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Finally, a speaker designer who intends to offer speakers compatible with high-output-impedance tube amps might want to keep the impedance curve as smooth as possible above the bass impedance peaks so there's no significant change in tonal balance from one amp to another, and perhaps also tune the speaker a bit lower than normal (or offer that as an option) to take advantage of such amplifiers' increased power output in the deep bass region. Here's what the impedance curve of such a speaker might look like:

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I took another set of measurements as well, using cone midrange drivers wired to present different impedance loads, comparing how these two amplifier types behave into different fairly smooth loads (4, 8, and 16 ohms). If anyone would like to see those, let me know.
Duke