@daftcombo I'm procrastinating on another task I'm finding tedious, so I thought I'd write a quick intro myself to interpreting step responses
Here I'll try to illustrate with some idealised examples.
Firstly, here's a two-way speaker in a sealed box with an F3 of 40Hz and an LR4 crossover at 2kHz. Let's assume it has a more-or-less flat frequency response, i.e. the outputs from the two drivers sum correctly on the measurement axis.
The first peak at 1ms is the output of the tweeter. It's initial rise is positive, from which we can infer that it is connected in positive polarity.
The second peak at about 1.4ms is the output of the woofer. Its initial rise is also positive, so it must also be connected in positive polarity.
Since both drivers are connected in the same polarity, we know this is not a 2nd or 6th order filter (which would require each driver be connected in opposite polarity in order to sum correctly).
We can see that the output of each driver integrates smoothly with the other. The two drivers are time-aligned.
If this were a first-order crossover and the drivers were time-aligned, we would see only one peak (as the outputs would sum to linear phase). But here, we have two peaks. So we can rule out that it’s a first-order crossover (and we've already ruled out that it's a 2nd or 6th order crossover). From this, we can infer it's a 3rd, 4th, or 8th order crossover.
With an 8th order filter, you’d expect to see more ringing in the tweeter’s output prior to the peak of the woofer’s output than you see here (and the woofer’s output would also be delayed more in time). So from this we can infer that we’re looking at a 3rd or 4th order crossover here.
At this point, it would be hard to know which of these it is, but if we looked at the vertical polar response and saw that the off-axis nulls were located equidistantly from 0°, from that we could infer that it was not 3rd order (since if it were, the lobes would be tilted downward). That leaves us with a 4th order crossover.
To illustrate how this graph might look if the speaker were designed differently, here is the same hypothetical speaker in the same box, but with a 2nd order crossover at 2kHz this time. Note that the woofer's initial rise is now in the negative direction, because it is now connected in negative polarity:
And now the same speaker with an 8th order crossover. The woofer is now back in positive polarity, but note the significant ringing of the tweeter before the peak of the woofer, and also that the woofer's peak arrives later relative to the 4th order crossover (which in turn arrives later relative to the 2nd order crossover):
I realise this is not particularly comprehensive, but hope it helps some