How can I split in half a double-page scanned PDF in a single pass?

There's an excellent, free and open source tool called Briss. It is very simple, user friendly and effective. It works on multiple operating systems through Java.

Load your PDF into the app. The app will group similar pages together and lay them on top of each other. Draw rectangles on top of your pages so that they cover what you want included. It will look like this:

Even if your PDF has multiple categories of layout within a single document, Briss will handle it. For example, let's say some parts are in portrait and others in landscape. Briss will group them into different categories and let you draw different rectangles on them, and then process it all in a single pass, into a single document. Briss is very good at deciding which pages should be grouped together. It typically takes me less then a minute of manual work to get Briss started. Thus, a document of hundreds or even thousands of pages can be done in a couple of minutes thanks to this brilliant program.

When it looks good, select Action, then Crop PDF.

Truly a very neat tool.

Note: I realize this answer reads like I'm a Briss developer or something, but I'm really not. I just love the tool.

You could use MuPDF's mutool:

mutool poster -x 2 in.pdf out.pdf