So I get this idea, could K4 be meant to stay attached to K3 during transposition to reorder the letters upon decipherment of K3 to put them in the correct order for K4 decryption. Instead of trying all of the letters at once, I wanted to do a proof of concept exercise.
Looks like it’s possible.
Not sure doing it this way would give you much for rearranging things. Might need to try an alternative.