They wouldn't synchronize any more! Only one of them "has a soundtrack" now in the multicam window, the other two are "mute" - but of course they aren't, I checked that, the clips are fine.
Now when I add an original unprocessed clip as a fourth camera and press "Audio Analysis", lo and behold, it works. After deleting this fourth track I can do my multicamera work.
So what am I missing here? This can't be the way it works, right?! Shouldn't I produce new (mpeg) files of the enhanced clips and just use them as they are after enhancing?