Design of the New Ship

Most weapon turrets can already be fired from the bridge, but in Traveller, if a Pilot or a Navigator is forced to fire the ship's weapons it means either a reduction in Pilot or a reduction in Navagator, depending on who you are on the bridge. Since Gevaudan is acting as both Pilot and Navigator, his skills in both are reduced by one. The rules stated that he cannot pull off three positions. Turrets have to be manned because of a lack of artificial intelligence and intuition to fire at targets. They cannot be fired 'remote', as you say, as there is not enough room on the bridge to accommodate such. That space is reserved for avionics, comms, defense screen control, diagnostics, and the big navigation/astrogation computer. Each turret has a small, one-man room with acceleration couches in which to fire a turret during high-G, 'dogfight' maneuvers.
Ship's locker is usually near the bridge. This was done so as to lower the chance of mutiny.
The more area taken up by Machine Shops & Electronics Labs, Lounge ("Central gathering space"), and Public Head, then the less space there is for fuel tankage (drop tanks become expensive and lessen the maneuvering and Jump of the vessel) and cargo (the ship has to be able to pay for itself...merc jobs will not do it alone).
Since weapon turrets can be fired from the bridge, fixed-mount style, there is no need for extra specifically for the bridge. The limiting factor is the sophonts (humans and Vargr in our case), who can do only so much per person.
Your list is extensive. Kudos for thinking of all this. I am with you all the way on maxing out the Computer to /5 and having decent comm system. More important than those two, have you thought of defensive Screens? Our Artemis 2 does not have them. No shields means we take everything incoming on the armor or point-defense weaponry, and that is a drain on both money and offensive capability.
A good first list. Prioritization comes next.