We know that English can be revealed through various analysis techniques performed on an entire cipher text. But, if the plain text of K4 was divided into n parts, and each part was encrypted with a different keyword, and then the individual parts of the resulting cipher text were put back together to make K4 appear to be one puzzle, the English would be masked because the results of any analysis on the entire cipher text would be bogus.
I seem to remember something about Ed Scheidt saying figure out the masking technique, then go for the puzzle. So, there must be clues in K1-K3 about the masking technique, i.e. how K4 is divided.
