the 12K for its famous bass, and the V30 for its upper mids, both with the heavy magnet and similar sensitivity. they should balance well i reckon, without being too much of one or the other.
V30 and H30 is a well known 'good' combination, and as the 12K is based on the H100, based on the H30... well it seems like it could work. the two different drivers give a larger sound.
obviously i've never tried it.. but this is the what i would go for in your place, reading your post and so on. the good thing about mixing is that it won't be too dominating with the character of one speaker. obviously the combo will do metal, but i have an idea it might be quite nice for jazz and other styles as well. i like the V30 for clean work, and with the extra bass of the K12, it should be killer for jazz i think. obviously it will be a bold, modern sounding cabinet which you'll create.
anyway, 100% conjecture ;) just an idea...