Right now, I have a Logitech Z623 setup attached to my computer. It's running off an old Asus Z77 motherboard with onboard audio, soon to be replaced with either a Z370 or X370 board. I'll be making sure I get one with an upgraded Realtek chip, but we all know those chips are decent at best. Up until recently I was using an older Yamaha receiver to power some desktop speakers, but I wanted to save desktop space and got the Logitechs. Honestly, I'm regretting the switch, but I'm enjoying having my desk back.
On my work space where I have my laptop I switched to smaller speakers too. Even smaller than the Z623. Using the SonicGear Quatro 2 now - these have 2in drivers with dual 2in passive bass radiators. Imaging and response are good enough once properly aimed, plus I get more bass than on a totally open desk as mine has shelves which acts as bass trap. Bass is louder, slightly boomy but not to the point of individual notes getting blurred.
So I don't listen to my music LOUD anymore. I'm older, my days of tinitus inducing punk clubs are behind me, and I keep volume levels comfortable and enjoyable. All I want is to be able to drive my headphones without pushing distortion (the HD25 & HyperX need the volume pushed to 100% right now), and also handle any HP upgrades I might make in the near future, say up to 250 Ohm. I want to be able to plug my HPs into the DAC/Amp, have the RCAs mute output to my speakers, then unmute the speakers when I unplug the headphones. If I have to flip a switch manually I could deal with it, but I'd prefer it to happen on its own.
I know the Schiit stack is my best option, and I'm trying to justify the $200 cost, but with the holidays coming up and more important things to save for, I can't justify doubling my budget.
The thing is though I wasn't suggesting the Schiit stack so you can pour 3watts into each driver, but because of all your requirements. And as for power, again it's not about pouring more power into what headphones you have, but pouring enough clean power into what you have and conceivably upgrade to.
As it is the only device that kind of complies with all your requirements are the Fiio E10K and the Audioengine D1, but I tried these on the HD600 and didn't really like them. E10K was blurring the bass (even with bass boost off) and the D1 was blurring the barely audible bass. 250ohms isn't that much higher. And the thing is, even with 300ohms, given the sensitivity of the HD600, that was already fairly loud. Still not as clean as the low distortion sound of the O2 and the Magni.
If you'd limited upgrades to low impedance, high sensitivity headphones (or IEMs), no problem. The Philips X1 I tried worked well enough with these - any bass distortion I got was attributable to the headphones (ie I can still got it even with my D-Zero MkII, and probably even with my desktop amp). There's also the HiFiMan HE400S, which has more controlled bass.
Or at least,
hopefully no problem - these are USB fed, both signal and power. Any nise through USB and you have no alternative. If you were hoping to use the DSP chip on the motherboard, no chance on that either since they only work via analogue output or SPDIF output (ie the same chip handles DSP and SPDIF conversion). If all your games have built in surround virtualization, no problem. If you use Razer Surround on the rest of your games, no problem (I personally didn't like it vs hardware DSP and headphone audio encoded into games, and I can't even hear a difference with it on movies).
As it is instead of blowing $100 that can't do what you need it to you might as well use the built in soundcard on the motherboard (assuming you have one of those gaming boards that have virtual surround DSP and the decent output stage and headphone driver chips). These have waaaaaaaaaay more clean power than your Logitech's headphone output, you can hook up both speakers and headphones, and you don't really need the preamp control anyway since the Logitech has a volume knob on it, and unlike studio monitors or powered speakers, they're small enough to sit on the desk closer to your hand.
And while you might think the connections and switching are a problem, if you're using virtual surround going into a DAC-HPamp, you'll have to go into the sound suite anyway to disable it every time you switch over to speakers. If your motherboard uses the same analogue output circuit on the rear jacks and front I/O (assuming you have one of the decent motherboards) then it's not that much of a problem in terms of driving power either. If not, then just run an extension cable from the rear headphone output to the front so you switch out headphones there. The only thing you really have to put up with is scrolling down to the lower right corner to adjust the volume, but you can just set up hotkeys for that.