Holy crap, a 5.5 kHz tweeter crossover. That's ridiculously high even given the relatively low midrange-tweeter distance. Vertical dispersion is not likely to look particularly pretty in that range.
Yep, just like I suspected - dispersion plots are in the spec sheet, and in fact they look very disappointing for a modern speaker all around. This would be appropriate for something designed 30 years ago, not in 2017. Not even close to the likes of Genelec, Sennheiser (K+H) or JBL, or even a number of modern-day home hi-fi speakers, including advanced DIY designs.
As far as the "critical range" goes, this is generally considered to be the vocal range up to 3 kHz or so. People were generally reluctant to put their crossover frequency in there as it would yield angle-dependent tonality changes due to the kind of irregularities you can see in the LYD48. These days you can put the tweeter in a waveguide and cross it over deep (and actively / digitally at high order to boot), which helps a ton with these things.
Speaking of driver measurements, the world could use a lot more data points on the effect of current driving on nonlinear distortion, Esa Meriläinen style. (The paper was available somewhere, can't find it right now. He measured 2-tone intermod at nominal 1 W levels.) It is hard to guess how a large midrange dome like this would fare, the effect on a 1" dome tweeter was quite small. The speakers that seemed to benefit most were cones with voice coils wound on non-conductive formers, and it should be obvious that you would be well-advised to stay far away from resonance (or use an amplifier that transitions to voltage drive down there) - down there you're generally excursion-limited anyway, and those nonlinearities remain unchanged. Interestingly, by the time the speaker crossover includes substantial series resistance, that's moving towards current drive, too - so basically your average tweeter in a passive XO is already operated like that.
Here's a tip - if your measurement mic is as noisy and exhibits as much 2nd harmonic as mine does, try a regular large or small diaphragm condenser with a (largely) flat response and decently low noise instead. Yes, it has to be pointed more accurately and minimum distance will be a concern due to proximity effect if it's a regular cardioid, but chances are it'll do much better at picking up the harmonics due to lower noise floor. I've had rather good results with a lowly t.bone SC-400, a house brand 50€ fixed cardioid China LDC... guess I should be looking for its cardioid/omni bigger brother, the SC-600, which did quite well in a review. Not sure which other mics are using the same capsules (they look like readily available 32mm Chinese LDC jobs), the electronics are rather common (those with an internal low-cut switch, flat response with no special EQ apparently).