Disclosure: I have absolutely nothing to gain (or lose) from describing my experience with the Klipsch speakers under discussion. I purchased 2 pair to ensure that the first pair wasn’t a one-off lemon. Both pair were measured and resulted in graphs that were essentially indistinguishable from those available from popular reviewers out in the wild. That being said, both pair sounded TERRIBLE: exceedingly over-polished and unlively; without energy, sparkle, immediacy, and chime; under-bright; or: shambling ZOMBIE speakers.
Even after making the modifications in my first post (strikethrough text below), the Klipsch RP-600M II remained a spectacular disappointment, especially for someone with profound sensorineural hearing loss that has had great success developing bespoke speakers with tailored frequency responses to serve that portion of the population, which customarily require powerful mid-bite and sparkling highs. I maintain, the hard-of-hearing are sometimes better judges of speakers, as they are truly trained listeners with advanced powers of concentration, picking up on nuances that are masked for the average listener by complacency.
Is the Klipsch RP-600M II beyond saving?
I didn’t believe so.
Could the Klipsch RP-600M II become an earl of clean tones, or maybe even a duke?
The answer is an unqualified, ‘yes.’
Deep down, I knew that the cerametallic woofer was capable of aggressive mids; that the titanium diaphragm tweeter was capable of bright highs, if only the speaker could get out of its own, arrogant way.
It would also require that I apply some tricks that are anathema in the audio engineering world: To bring the speaker to life, rules would have to be broken — most of them.

First we ripped the speaker down, removing the woofer, tweeter and crossover network. The tweeter (6.5 Ω) was wired out-of-phase with the woofer (3.3 Ω), sans crossover network (typical in-house dipole wiring schema). The nominal impedance of the speaker then measured (2.2 Ω). The Yamaha plays well with low impedance speakers, as do our Class A-B Pioneer car amps (which, incidentally, if bridgeable, serve as exceptionally cost-effective mono-blocks), so 2.2 Ω was a perfect result for our purposes. Poly-fill was then added to the large cavity behind the woofer, but I did not fill it far enough to obstruct the tractrix port and tweeter cavity.
Results were nothing short of astounding for my purposes. Here is an SPL measurement at typical low-medium listening volume w/ microphone placed at the distance at which this listener typically sits. It’s important to emphasize, the crossover networks have been completely removed from the speaker pair (1/12 octave smoothing):

As you can see from the 90-degree off-axis measurement below, the out-of-phase wiring schema confers excellent dispersion characteristics and a broadened, full-range sound-stage to the 600M II (1/12 octave smoothing):

Finally, is the stock enclosure a tad too small for the current woofer/tweeter setup? I suspect it is, slightly, resulting in inefficiencies that may be easily addressed with the addition of poly-fill, per above.
Conclusion: The Klipsch RP-600M II can be a Duke of Clean Tones, but it requires a crossoverectomy and non-traditional wiring schema.
I wanted to post this as it may help folks who buy and find the RP-600M II’s sound decidedly over-polished and unlively; without energy, sparkle, immediacy, and chime; under-bright.
Current chain: Flac File (foobar2000, ASIO-mode) –> Topping E70 Velvet DAC in pre-amplifier mode –> Yamaha R-S202 Amplifier –> Klipsch RP-600M II (x2).
I utilize 2 sets of Mark IIs wired in parallel in order to lower the characteristic impedance of the speakers to 4 Ohm, then bi-amp to the Yamaha. That is, two speakers, stacked and wired in parallel for the left channel and two speakers, stacked and wired in parallel for the right channel.
Removing the jumpers, wiring 2 pair of Mark IIs in parallel and discretely bi-amping high and low drivers brought these formerly underwhelming speakers to life.
I hope you find this helpful.