Who decided Intrepid
was supposed to be 1631 or 1831 anyway? It certainly wasn't onscreen. Was it written down anywhere like on a script draft? It's been a very long time since I read Jein's article.
The only registries TOS ever established were the Enterprise
(1017) and Galileo
(1701/7). Anything else is pure conjecture or arbitrary unless someone knows of any notes somewhere.
Otherwise based on what we know I give the nod to FJ's reasoning.