So far, looks like it's gonna be 52004, which is a little low for the period, but hey, it's not a canon ship, so who needs a canon reg?
Here's a storyline to explain the design...
As things progressed with the design of the Sov, Starfleet realised it was time to start designing the next class that would have the name Enterprise. But, due to the untimely loss of the Ent.D, Starfleet was forced to use the newly completed Sov. design.
This can kinda explain the differences from the Sov and the more traditional look to the Titan, i.e. with the neck and all. What ya think? Please feel free to embelish the story.