From my search up here or else I found some short list of amps that suppose to be the best with K1000. Of course everything is subtle and a matter of taste, but all of them were speaker amps. That's why I suggested it to look for some budget T amps, which to my ears, for their price, cant be beat it by any other, but can drive K1000 with ease and deliver quite musical sound. I cant suggest anything else where I don't have any experience, yet, include the founded list, so I dont post it to avoid wrong impressions from my side.
Once again, I tried K1000 with EAR HP4 and they were far away form loosing their dynamics or anything else, its just for that kind of money, or even less, you better be of with the speaker amp, imo.
I am going to check some amp, integrated tube speaker, and if I like it will post some later.
p.s. Guys, if you have the expiriance with general SE headphone amps, which can drive K1000, why wouldnt you post the list.