This something that would be useful in a variety of contexts for me...

I want to define a shape, and have that object make that part of its layer transparent.
Essentially, I want it, for its position in the Z-order, to override what is below it
in the layer. So it's sort of a 100% opaque, transparent object.

Perhaps an example will help explain what this means. Let's say I have straight line
segment path with a bunch of pointed corners. I want to cut off the corners just so.
If the background color of the drawing were white, I could just make some white
rectangles, and put them here and there cutting off the corners. The path would
appear to have angled corners instead of pointed corners. But what if the background
is an image? Then I need to cut the path. I'd rather not do stroke-to-path as I lose
the ability to move the path around (yes, I'd have to move the rectangles, but still
easier). Wherever one of these rectangles was, the layer would be transparent,
unless something higher in the Z-order overrode that.

Another example use would be modified typography on a background. Say I want
to "antique" the text (cutting out bits here and there). Fine, again, on a white
background, but not fine with any image or textured background.

Although not quite as easy to use as what you want with the "transparent object" things, have a look at clipping paths/masks or 1.

Thanks. Know about clipping path. Didn't think of using it in this case. Not a bad workaround, though still hoping for someday ...

As i understand it a layer in Inkscape is really a group (although the layer blending modes add some considerable additional functionality) You can group and clip the group or select all in a layer and use the topmost or bottommost object to clip.

I want to define a shape, and have that object make that part of its layer transparent.

This would definitely be the mask function. It's a little more complicated than clip, but has all the functionality that you are asking for... you would need to make another shape that is larger than all the objects you want to mask , fill it with white, fill or stroke your masking object with black, move it above all objects involved, group it with the large white filled object, select all, set mask and it should be what you want...

Thanks, druban! Might take me a bit of experimenting to see if that is what I'm looking for.