While I have no doubt as to the variance of K1000s dependent upon manufacturing dates, I would imagine the β22 would be well suited to all varieties. We're talking about a very neutral amp here, and the β22 has the grunt needed for these phones. I think the way to approach a K1000/β22 system would be to find your particular flavor of K1000, not to try to correct a variety of K1000 you might like less than others by trying to tailor an amp to mask those less desired characteristics.
I would have loved to hear Naaman's B22/K1000/Buffalo system. This is where I'm headed source wise, though I've not heard any of the Buffalo varieties. I doubt I'll be disappointed though, as so many people I seem to agree with on most things have raved about the DAC.