Messing up textures and cycles tiling

So, I’m working on messing up textures with imperfections etc, and here’s where I’m at with a test scene (though knowing me it will eventually grow into a full scene).

However, it leads me to a question. The wipe marks on the tiles come from an image texture. The texture itself is high res (2826x2848), but is too large detail meaning that it’s tiled across the UV.

In the render, I created a tiled version in GIMP, and have used that. However, it’d be nice to use the original and be able to blend an offset version randomly. I can do he random with a gradient and noise, but I have no idea how to get a blend similar to the blend in box projection mode. Anyone have a node setup to get a smooth blend that does the same on a tiled flat projection?

The original texture (i.e. not the tiled version):