Turns out my config was all right. The problem was the test message, which was not identified as e-mail. When I got that right, it all works.
I simulated incoming emails via transaction SOIN: Utilities - Import MIME. At minimum, the file must contain the heading Subject: and then some text. The subject heading was copied to Subject field in SAP's e-mail object. The rows that followed the subject were interpreted as the e-mail body, and with our config, it was copied to Description.
From there on, the e-mail contents were copied to the follow-up transactions, such as incident.