"Mon" means clan crest or emblem, not the banner as a whole (upon which the mon is often printed). The armies of the Sengoku period often carried banners in colours completely different than the armor or clothing they wore. And they carried more than one type of banner on the field.
For the Date banner, I followed the black mon on white background idea from both Danborg a.k.a. TomteOfDoom, who's very knowledgeable about this period in Japanese history, and the image shown in the OP regarding my sources for the Date, which I found on a site covering Japanese heraldry. You may want to take a look at that image again. As far as I can tell, it depicts a Date army on the move, carrying lots of different banners. As you can see, more than one type of mon and low in the middle of the pic, there's even one with Date's "principal" clan mon in white on black background.
Other pics from the same dedicated source suggests that four different colours could represent the Date: white, black, indigo blue and yellow (gold). I'll work something out with these options.
Whatever I come up with in the end, no-one is faced with an "accept all or nothing" situation regarding my mods. You can always edit them to revert back to vanilla or some other choice using PFM. I'll add instructions about how to do that at the end of post #3 later, as I keep getting requests about some change or other to my mods.