AFAIK Intrepids NCC number comes from this chart nontheless. Okuda did not have access to images that high in resolution as we have today and misread the eight in NCC-1831 on the chart as a six.
Greg Jein is the one who misread the "1831" as "1631" as the resolution of his film still didn't yield more information back in the 1970's when he wrote his treatise "The Case of Jonathan Doe Starship" (heck, even in HD today I can't determine whether it is "1664" or "1864". Trying to examine the scene still by still in Full HD resolution it changes back and forth between "16" and "18"...).
Bjo Trimble's Star Trek Concordance
adopted Jein's numbering proposal, same as the Okudas for their Star Trek Encyclopedia
(and during the days of SD resolution, I should add).
However, the Okudas were involved in the TOS-R project and thus had access to the starship status chart in HD before most of us. If there's one thing that has become crystal clear, it's that the number is "1831" and not "1631".
Of course, the Okudas could have decided, not
to reveal a new CGI shot of the starship Intrepid with
the registry number. The moment they did ("1631"), they practically "pulled" the Intrepid
from the starship status chart and changed its possible meaning.
Personally, I don't consider this to be a final word (because I've mentioned other reasons why I doubt the chart reflects repair work), but felt it to be worth mentioning.