Good God, that's a fun puzzle! These surfaces have a real clear (and fun) voice, and they were a joy to solve, particularly 1A and 6A. I also really got a kick out of the lift-and-separate in 3D; I might've made it [kitchen-dweller's] to be more of a sentence, but I can see why you didn't.
The only one that doesn't work is 2D, which I'm pretty sure is an overlapping root: it's called INDIA ink because of the country that exported it, right?
Thanks, Aaron! When it came to 1A, I was hoping people would read it in James Brown’s voice like I did . And 6A took me the longest to construct; I was hoping to come up with a wittier rhyme for my clue but had to say “Good enough.” and use the punctuation to make it fairer to the solver. Regarding 2D, it is my understanding that it is an industry and commercial term for ink produced all over the world, and the earliest known use was in China. Granted, England was acquiring it from or through India at the time it became popular. I see how this could qualify as an overlapping root.