Filling in about K-888. It was some time since I last used it, but given the correct negatives it's a beutiful paper. It's really responsive to different developers and procedures as the OP says. While the highlights are ok, the shadows really pop out of the print. All in all, it has all the typical characteristics of a chloro-bromide paper, i.e. it's slow, responsive, develops in 3-4 minutes, rich in tones ... In other words, more or less the opposite of e.g. Ilford Galerie, which comes out more or less the same regardless of developer choice etc. (Galerie is of course also rich in tones, but it simply "develops, full stop" when compared to e.g. K-888.)
The downside... Yes, there is a downside. QC and consistency with Emacs papers is terrible. The grades varies a lot and you simply cannot get another box of the same grade and expect it to be the same. The "solution" if you like the paper is to get hold of rather large batches from the same roll and store it cold. Second, as I mentioned above, the paper is slow, especially grade 3 which is so slow ... coffee ... and another cup ... before you've exposed it enough.
Some well-calculated pre-flashing may do wonders, but will also render a softer grade paper.
//Björn