To KrytosFreak- You don’t have to call this cipher Vigenere. Call it a varient Beaufort cipher. Its interesting to note that the Y-A-R in K3 can also be solved with this cipher and results in the plain text CIA using abscissa as the pass key. This could be a clue to use this version of the cipher.
I agree with OAXX, Why spend half your time creating the copper plate with a Vigenere alphabet matrix if its not to be the most important cipher in this puzzle. The fact your not considering a Vigenere or some variant of it seems more dumbfounding.
Back to OOAX- I stumbled upon this idea shortly after the BERLIN clue was announced and worked on it pretty extensively as far as looking for a continuing sequence but I have not just looked for random words in the PT and tested them in all the possible K4 positions. My brother who is a computer programmer said he would put something together to find as many words or partial word combinations as possible in the K1-K3 PT matrix and then grab the corresponding key letter sequences from the CT and test them in all possible positions in the K4 sequence but he has never done it. So I’ve tried to explore other ideas occasionally coming back to this. I just like this idea because it contains a Stego step and has a visual element both of which have been hinted or stated outright to apply in solving K4.