I checked the same wiring diagram for my 3/14/2007 build 328xi (N52) and it has the ground to the DME Relay being provided by the same Pin #13 of Connector X60005 at the DME, BUT the wire that goes from Pin #13 of X60005 IS White/Gray, just as your photo #5 shows, with wire separated by small (HFT?) pick. BUT, on my 328xi N52, the color is RED/Gray on the other side of X60551. On your 335xi, is the wire to which the White/Gray wire from the DME connects at Pin #5 of X60551 Red/Gray or White/Gray (on the OTHER side of X60551)?... I've reviewed TIS schematics vs. the physical wiring in the car and the color wiring does not match. First: DME connector X60005, pin #13 is not RED/GREY, it is WHITE/GREY... Second: Connect X60551, pin #5 is also not RED/GREY but WHITE/GREY. [??] ... At this point, I have not attempt to ground any pins as a precaution but the cable colors do match. Do I trust it? Also if I was to apply ground, I believe I would be applying it to the female side of the X60551 since it seems to go to the JB vs. the male side which stays in the E-box.
There is so much detail in TIS wiring diagrams that there are bound to be errors. I get as "spatially-challenged" as the next guy. If you are going to be getting a multimeter or you can scrounge up one or a test light (anything to test continuity of a wire), what I would suggest is testing the White/Gray or Red/Gray wire that runs from Pin #5 of X60551 and leaves the E-box, to see if that is the same wire (electrically-connected) as the wire (whether Red/Gray or White/Gray) that is found at Pin #1 of Connector X11010 at the top-Left of the JB fuse panel.
That is, after all, what we are trying to apply a ground to, in order to test the K6300 DME Relay. You could always just apply a ground to that pin on the top-left of the JB to test for Click & Voltage at Terminal 87, but we also need to test for ground at Pin #5 of X60551, AND for continuity between Pin #5 of X60551 & Pin #1 of X11010.
Perhaps I'm missing something, but if you have X60005 disconnected from the DME, I don't see what could be harmed by applying ground to ONLY Socket #13 of X60005. ALL we are trying to do in this limited test (with X60005 disconnected) is to test relay click and any Terminal 87 Activation.
Here is the Installation Location of X11010 at the JB, and the Connector view showing location of Pin #1:
Hang in there. The fact that you have the confidence and concentration on details to "proof" TIS suggest you will be able to solve this puzzle.