Export parts of a scan as separate images in Lightroom?

Yes, Virtual Copies makes it so easy.  [Ctrl+'] is the VC shortcut.

One way to do this is to make virtual copies (Photo > Create Virtual Copy) equal to the number of stamps, then crop each virtual copy differently, then export them all. Virtual copies are great for this, because there will still only be one real scan file.

Advanced tip: Because a virtual copy is not a real file until you export it, it doesn't have a unique original file name. But you can name them so that they do have readable unique file names when you export the finished versions:

1. Switch to the Library module.
2. Choose EXIF and IPTC from the pop-up menu in the Metadata panel header.
3. For each stamp, fill in the Copy Name field in the Metadata panel. This should be whatever you want the final name of each stamp to be.
4. In the Export dialog box when you export all of the cropped virtual copies, use the File Naming panel to rename the exported files using the Copy Name token.

I called that an “advanced tip” because it requires familiarity with the Metadata panel, the Export dialog box, and the token-based file renamer in Lightroom Classic. But it’s worth looking up how they all work.