Although I've never heard the K1000s, one thing seems overwhelmingly obvious to me:
THESE HEADPHONES ARE JUST BEGGING FOR A DHT OUTPUT STAGE!
If you have never heard an amplifier that uses DHTs (Directly Heated Triodes) in the output stage, you are really, really missing out. Especially push pull versions. Mastergill reccommended the Manley Stingray that has a Triode output stage. The Stingray uses EL84s, a PENTODE tube, operating as a triode. This is accomplished by connecting the screen grid of the EL84 to the anode. Sure it sounds better than Ultralinear operation, but it still doesn't beat a true triode, and an Inderectly Heated Triode doesn't beat a DHT.
A well designed Push Pull (PP) DHT amp, in general, sounds better than an SET (Single Ended Triode). I've heard the difference. People rave about SETs, but a PP amp can have everything a great SET has and more (namely more controlled and powerful bass).
There are a few makers of PP DHT amps. Deja Vu Audio (incidentally in McLean, where I live) makes some of the best. Look them up. Check out their site at
www.dejavuaudio.com. See if you can get a hold of the owner, Vu Hoang, and ask him about his amps. They start at $5000, I believe.
You want my opinion? A PP amp using 45s (the tube type) would blow everything else out of the water with the K1000. A PP 45 amp would output around 2 or 3W, plenty of power for these phones. 2A3s sound almost as good, and 300Bs, despite what people think of them, aren't even close.
I sincerely hope you don't drop 5K on that EAR without even looking into anything else first. Just because one person says something is the best (even if it's Todd) doesn't mean it IS the best. I guess this would apply to me too, but my opinion is a fairly widespread one. And I REALLY mean it.
PLEASE don't buy a $5000 amp without spending some time researching your different options. And for God's sake, at least TRY to listen to some amps before you buy one! What kind of person decides to drop 5K after only a couple hours of consideration, without even making sure he likes what he's buying?!