JES, perhaps my opinion is clouded by the game I'm familiar with, but that's a heck of a lot of weapons for such a small ship. All the source material I've ever seen (two games, three different sets of blueprints, etc.), gives the Constitution-class cruiser four photons and three pairs of phasers on the saucer plus another pair on the secondary hull.
I would propose that this ship have two photons forward (but not in the bridge bubble ... I hate that idea as all the TV episodes have the photons coming from the under side of the saucer), twin phasers forward, singles phasers port/starboard, a single phaser aft, and twin point-defense 360-deg phasers on the ventral of the aft hull. A war-time upgrade would probably twin up the side and aft phasers and add another pair of 360 point-defense phasers on the dorsal.