The reason I want to export the images is to do exactly that,
Do you mean to say that 131072 x 131072 px is the size of one of the slices? If that's the case, then just make smaller slices.
Or do you mean that you want to use some raster program to slice it up?
Also, as I re-read this thread, I wonder if you could be confused between size and pixel density? Are you adjusting the DPI in Inkscape's Export PNG dialog, thinking that you are adding more pixels to it? Inkscape works a little bit differently than you may expect.
When you change the dpi in the Export PNG dialog, all it does it make the image larger. It's only after you print, when you set the size for the image, and then the pixels get compressed down. Or load into a specific size of html "frame" on a webpage.
But, if that's not the case, then just ignore the last comments here