Okay, here's what I'd like to do, and can't figure out how:

I've made an image, white with a black background (alternating white and black layers). The image is mostly white but parts of it fade between white and black so it's actually greyscale. I would like to make a copy of it to overlay on images in such a way that the white parts are solid white (full opacity), the black parts are completely transparent, and everything in between is the appropriate relative transparency. For example, the parts that are 50/50 would have 50% transparency.

Is this something I can do in Inkscape?

Hi.

You can use filtering for that. Setting the layer to screen blending mode would be "close enough".

If not, try applying this filter on the objects grouped together:

You could also use the existing image as a mask over a white background. Gather all the bits of your image together into one layer, and group them. Then draw a white rectangle that covers them all, and send it to the back. Finally, with both the white rectangle and your B&W grouped image selected, use Object > Mask > Set.

Turning on the checkerboard background in Document properties might help to confirm that the right bits are becoming transparent.

Xav, that did exactly what I was hoping! I need to look into "Mask" more...

Blatant plug: Part 14 of my tutorial series covers masking.