Hi Michael.

The first one is pretty correct - we're aware of a number of Carreras in the 53xxx and 54xxx range, but these usually have round screw backs rather than the poly casebacks we find in the 56xxx range. The hands may have had some seawater moisture at some time, which can leave green copper deposits on the lume but it looks a bit too uniform for that and doesn't match the other lume plots so I'd agree it's probably a relume. Case looks a little bit polished from what I can see of the lower lugs but still decent enough, and an unsigned crown is not unusual this early (though going by the chamfers on both leading and trailing edge, I'm not sure this is the original).

The other is a second execution Carrera dial, but it's not in a Carrera case at all. Looks like it could be a 2444 case:

which model just overlapped with the Carreras, although a 56xxx serial is a shade higher than I'd expect for 2444 not still well within the bounds of possibility. It would still put it in the Carrera launch year and Heuer didn't expect the Carrera to do as good a job of killing off the rest of the range (bar the Autavia) as it did.

Unfortunately, this was before the model reference was added to the cases but if I were a betting man, I'd say 2444. Looks like 2444 pushers too. The inner bezel on that one isn't a Carreras either unfortunately, or you could just do a swap.They do come up for sale occasionally, but they're pretty sought after as a common source of "failure" on first gen Carreras (the paint comes off, seems a bit harsh to call it an actual failure).

If you wanted to find a proper Carrera replacement case for the black dial, you'll be after one with a serial around 93xxx and above.

Hope that helps!

Mark