I was trying to work out how I could shade the whole thing just a tone darker, and what I did was this: Take an empty paint pot and put a small bit of Nuln Oil (Black GW Wash) in it, then add water, with about a ratio of 1:6 or 1:10 or something like that. I just used an eyedropped to grab a little but of nuln oil, then filled the pot about a quarter or a third with water.
Then I washed the whole surface with this very watery mix, with a large wide brush (I just used the Citadel Large Drybrush for stuff like this). It gave it a nice stained/weathered water stain look, just a few shades darker than how it was yesterday, but enough to make it blend in better now with the rest of the building. Because it was mostly water, it didn't leave brush strokes behind, which was good.