I got it, it was a typo! Copy-paste error.
I made two new interfaces, and after the copy-paste, I haven't changed the names in the annotations of the *Bean.java files:
@Stateless(name="PersonManagerService")
I don't know why I looked over these, but unfortunately these are strings, so the type system couldn't detect this error.
Another conclusion: the consol output provided less verbose output than the server.log, so I should look at that thoroughly next time. I spotted that a class name mentioned two times in the server.log during the EJB deployment, shortly after my quoted log section. That's how I found the error. I was looking at server.log before, but not thoroughly enough.
Thank you for your help!