Shaw, thanks for this very informative information. The only thing I could add to that would be that it's *possible* that we know the Intrepid's number too, if one extrapolated from the chart in "Court Martial" that the NCC-1831 was meant to be that ship, per the dialog stating that her repairs are complete.
EXCEPT, there is no dialogue stating that.
Here's the line:
Nothing there to say that repairs are complete, only that Enterprise ranks higher on the priority chart.STONE: Maintenance Section Eighteen. The section is working on the Intrepid. Reschedule. The Enterprise is on priority one.
As for how readable that chart is, well, here's the clearest high def pic of the numbers of that chart on trekcore.com...

Sure looks like "1831" to me. And since Okuda and his team had access to the actual footage, I'll trust his account of what's on that chart.
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