Okay, so I trashed the Logic Pro preference files in:
~/Library/Preferences/com.apple.logic10.plist
~/Library/Preferences/com.apple.logic.pro.cs
This meant I had to re-adjust my Logic preferences (including any custom keyboard shortcuts), but at least the question mark (and other devices) are now gone from the MIDI > Inputs tab.
If in any case I see the "Error initializing Core MIDI" again, I will post it here.
For now this topic can be marked as solved.