E09K is not a DAC, it just works as an amp, you have to use it in conjunction with the FiiO E17. For the price it's not bad, I still have it but rarely use it nowadays. I never heard the HD-650 and for sure the Emotiva has a lot of power for it and there's an impedance mismatch as it's nominally 300 Ohm (but being a dynamic headphone this may drastically increase at certain frequencies), my HD-800 is also 300 Ohm but it goes up to 700-800 over the band.
As for safety of driving it over the Emotiva: provided it matches well with that amp (sound quality) then I think there's little danger if you're VERY careful with the volume. As you rightly remarked, your eardrums will go before a driver does. Also, only connect them to the amp AFTER it's been switched on, don't just leave them connected as a power-up peak could cause damage. That's just my 2 cents worth, I don't own either the Emotiva (not a fan of using speaker amps to drive headphones) nor the HD-800.
As to the project Ember, no experience there, personally I'm not a fan of hybrid SS/tube designs but that's just a question of preference. What I use (apart from my V800/V200 SS combo) to drive my HE-6 is a Darkvoice 337 tube amp, that's a dual mono design I purchased used 6 weeks back, never thought it would work well (power) with the HE-6 frankly. My 337 was modified and the maker doesn't specify precise power output figures, I posted about my astonishment in the 337 thread here. Then I mailed the company and asked, turned out that one of the headphones they used while designing it was...the AKG K-1000, which must be THE most inefficient design ever produced, at 74 dB sensitivity. Anyway, my point is that if you want a relatively cheap used system that'll drive both your HifiMan and Senn cans nicely then it's worth checking out e-bay. Just be careful if you want to use it to drive low impedance dynamic cans, not sure if it plays nicely with them due to the output impedance mismatch. But I can testify that it works very well with my HifiMan HE-500, HE-6 and the Senn HD-800. And you have more tube rolling options than with the ember.
