So Ed Scheidt already told us that we can’t treat K4 in the same way as K1-3 and that our understanding of and the math of the english language will not be as helpful. It does not seem to resemble a transposition or substitution cipher. Possible it is a polyalphabetic cipher as the ranges are flattened out.
We still need to check the letter frequencies if nothing else but to know for sure. If my counts are off, please let me know, but this is my analysis of K4.