: Maybe the case was polished / reworked, maybe it is a fake,
: maybe the inscription just rubbed off with time...

Possibly. There should always be a serial number on a 2447 case.

: In any case, it's a pity that there isn't (yet :) ) a Carrera book
: or at least an online detailed comparison/timeline between
: what's right, what's not and what was produced by Heuer, but I
: get that these were difficult times to catalog,

There's quite a lot of info on OnTheDash, including pictures and the chronograph table. It's a good place to start. Richard Crosthwaite and Paul Gavin have produced a book on the Carrera, check it out.

: plus, the
: Carrera is a difficult watch in itself (for starters, they don't
: have a serial number...)

Umm, they do have serials? If you mean the model reference, that is also engraved on later first generation watches.