In the 5 or so years I've been using the Epson oscillators I've looked at the spectral output many times.   Without a doubt the harmonic output from the Epson oscillator is high as would be expected  from a square wave device.   The question to me has always been "does it matter"?

PLL controlled digital oscillators have long been used as LOs in receivers and transceivers, including the Si570 and Si5351 which also have square wave outputs with high harmonic content, so I felt the Epson oscillators should be no different, and that has been my experience.    I've also used the clock generation capability of the Raspberry Pi extensively for wspr, which is also a square wave signal that is nicely filtered by use of a  7 pole low-pass filter taken straight from the GQRP harmonic filter guide.    I've also designed my own lowpass and bandpass filters for wspr using Elsie which  work equally well with spots from around the world using 40 milliwatts of power.

All of which is to say - if you want a clean output directly from the oscillator you will need a filter to remove harmonics.   However my primary interest in using the Epson oscillators is for crystal replacement in radios where they either provide injection to a mixer or drive amplifier stages, all of which already have tuned circuits that are resonant at the frequency of interest.   I've done the comparison vs quartz crystals numerous times and the answer has always come up the same:   the spectral purity using the Epson oscillator is no different from using a crystal.

That said, we all know that merely using a crystal guarantees the absence of harmonic content (which is why hams have used low pass filters and sometimes received pink tickets!)    But my point is that the harmonic attenuation provide by the transmitter is the same with a crystal or an Epson - it's a function of the transmitter itself.    Many hams use antenna tuners nowadays which provides additional high selectivity to prevent whatever harmonics may be present from radiating far.

Today, FCC part 97.307 requires 43dB attenuation of HF harmonics for radios built since 2003,  40dB for those built between 1978 and 2003 (30dB for < 5 watt rigs), and those built prior to 1978 are exempt.   Even though crystal replacement in boatanchors is thus exempt from 97.307, it's always been my goal to at least come  close or if possible to meet the FCC regulation, or at least to be no worse than the same radio is using crystal control.   Attached are three comparisons of  Epson oscillators showing the spectral output for various configurations:

1.   Raw Epson vs. G-QRP LPF.    This shows the attenuation provided by the 7 pole 20 meter LPF per the attached design guide.   While the harmonics are still present, they are attenuated by around 40dB.

2.   HW-16 - comparison showing there is no difference in harmonic content whether a crystal or an Epson oscillator is used (this is with the Epson oscillator driving a one transistor broadband amplifier of my own design).    The second harmonic is down about 38dB and the third is actually better than the crystal.

3.  Bendix Skipper 101 Marine radio.  The "crystal" spectrum is the normal  2-tube transmitter using a a 12AQ5 oscillator driving a 12JB6 PA for about 20 watts output.   The second plot shows the output of the untuned amplifier connected directly to the grid of the PA tube, bypassing the crystal oscillator stage in he the radio entirely  (it is also untuned).   No difference in harmonic output can be seen with both providing about 36dB attenuation of the second harmonic.

4.  My experience says that tuned circuits in radios are highly effective at removing harmonic content when Epson oscillators are used to drive tube type transmitters and all kinds of mixers.   A parallel resonant tank using a 2.2uH inductor and combination of fixed and variable capacitor was adjusted to resonate at the 13.85MHz frequency and coupled it to the output of my untuned amplifier.    A two-turn link enabled the spectrum analyzer to create the "tank" plot which shows about 30dB attenuation.  (I would also note that this was a "lash-up" of two existing boards using short leads but not optimal RF wiring and grounding practice and a properly designed tuned RF amplifier could no doubt be even better).

We use class C RF amplifiers because they provide high efficiency, but at the cost of high harmonic distortion.  That's why they are invariably used with tuned loads that are resonant at the frequency of interest.   So even if we fed a perfect sine wave into a class C amplifier, it will create it's own distortion that must be filtered out.    To my way of thinking this is why none of the transmitters I've tried Epson oscillators with cares whether the input waveform is sine or square -  the class C PA is biased such that it is conducting less than half the time and relies on the flywheel effect of the resonant tank to keep the sine wave going during the non-conducting portion of the cycle.

If you use the Epson oscillators in a stand-alone mode or with an amplifier, I strongly suggest using either a LPF or tuned output circuit in the amplifier - the data presented here offers a guide as to the degree of spectral purity that can be obtained using LPF and tuned circuits.   But for general crystal replacement, it is clear that the harmonics present in the square wave output have no more impact on harmonic generation from a typical transmitter than when using a quartz crystal for frequency control.