Update, in case anyone is interested.
According to the USCG Documentation
office, a vessel may only be documented or state registered, not both. The way the rules are written, the title is null and void, and should be surrendered (or shredded).
Just another instance of state DMVs have no concept
of what a documented vessel is, and being clueless about the laws. Either that or they're just trying to milk a few more dollars out of boaters for an invalid document, that's good for nothing except maybe wiping you ***.