That was my original intent for the Brattain when I surmised a chronological registry scheme: That there's no way the ship could have been constructed in 2345, for several reasons, one of which is that two ships with registries of 3XXXX and 4XXXX (the Intrepid and Wyoming, respectively), were already in service when the ship was built. Therefore I surmised that the stardate on the dedication plaque was just incorrect, or from a different, older stardate sytem than the current TNG version. There is evidence the system changed at some point, such as with some of the dates you mention.
However, with a batch number registry scheme, it could possibly work (at least, based on the batch number scheme I personally came up with, based on several factors). I will post it separately.