Custom projection matrix: part ortho, part frustum

I’m trying to create a projection matrix that
behaves like an orthographic projection for the y coordinates but behaves like a
perspective projection for the x coordinates.

Another way to explain it is that instead of
a pyramid shaped viewing frustum, I want one
where the shape is a wedge.

At first I thought “Hey, no problem, I just
have to derive the right matrix and I’m
there.” But after looking it how the coords
are divided by the w value (the perspective
division) I’m beginning to wonder if this is

Does anyone have any ideas?