My view on the interconnectedness of K1-3:
K1: the last word corresponds to the date 11/26 at the position of the Q.
K2: the last telegraph segment gives us an instruction relating to the horizontal components of K3, XLAYERTWO.
K3: the last sentence is bounded by two superfluous characters, X and Q, which I believe are the keyword hint for a new Vigenere tableaux, since Sanborn mentions in an email to NYTimes journalist John Schwartz that he uses a table that is slightly different than the one on the Kryptos sculpture.
At the end of the day, Sanborn is an artist, not a mathematician and not a cryptologist, which is why I'm shifting things up now and doing my best to keep out of complicated things such as the straddling checkerboard. I took a moment to rewatch the 12 minute Nova segment and noticed something that might be a hint about the Tut mask. On 1:32 Sanborn says "so you're the CIA? That means you have nothing pulled over you're eyes...," this made me think of mask over a face. This is the same video where you'll notice the PCPCPCPC note in the margin of the solved K3.
I think Sanborn uses the words of K1 as a way for us to make the connection to the use of a calendar containing major lunar phases. The moon when full is something which reflects the light of the sun and when it's in the new moon phase it actually interrupts a small portion of the light of the sun in it's transmission to the surface of the Earth. K2 has 9 interesting characters: 1) the second U of UNDERGRUUND fits the date location for 9/24, 2) there are 3 ?'s and 5 X's that are superfluous to the text. K2 having exactly 365 characters when removing the 8 superfluous characters is ideal for a calendar system. I think those 8 additional characters are the hidden hint that the keyword for the new Vigenere tableaux will have 8-letters between the X and Q hinted at by K3. This 10-letter word X********Q is Ceasar shifted from YTIVITALER. This is a guess based on finding the only year for a new moon occuring on 9/24 in the 20th century prior to the installation of the sculpture and then asking what was one of the greatest discoveries of that year and what does it have to do with light and shadow?
So I think we take the word RELATIVITY and we create a new Vigenere tableaux. We then use this tableaux to create the mask. The first 42 letter row of K3-solved correspond to the "P" or plaintext letters found along the first row of the table and the second 42-letter row of K3-solved corresponds to the first left-side column's "C" or ciphertext of the table. Find each interior letter for each P and C and that will be you're mask of 168-letters.
Next, take the K4 letters and apply each to the interior of the table as the correspond to the mask-letters as they apply to the first left-side column. I believe this system will reveal our plaintext solution. The challenge fo r me at this point is figuring out where the starting point is in lining up the 97-letters of K4 with the 168-letters of the K3-mask.