You know, I think a TOS-style deflector inside the TMP-era Excelsior "deflector housing" might look pretty neat. If you make the deflector dish quite a bit smaller diameter (like the Excelsior deflector), and upright (not slanted as it currently is). Make the indentation on the hull circular, rather than the awkward "oval" of the TMP Excelsior, with it being narrower on the inside, and have a wider opening at the "mouth".
You have the makings of a great looking ship. Just would like to see more classic Excelsior style elements to it.
I also agree with your concept, that the ship might've been in use long before we see the first reveal in ST:3. The Miranda Class which is a contemporary to the TMP Constitution, is another one of those that must've been around already in TOS, and been refitted to similar standards by ST:2 (and beyond).