For your helmsmen, I caught a reference in "The Catwalk" the other day where Archer told Mayweather he'd be relieved by Tanner. Turns out Tanner has a history as relief helm. http://en.memory-alpha.org/wiki/Tanner
Historically captains are not assigned to a watch, they supervise all the watches and are available whenever needed. On all but small vessels, the same goes for the XO.
Hoshi doesn't get to be the Chief Communication officer? She practically invented the Universal Translator and is a linguistic savant.
I still think you're WAY officer heavy, but... Trek does that so it would be overlooked by most. I would actually see a lot of overlap between the departments. While everyone has a primary station they help out where needed. Security people would regularly be helping out in engineering when there's no fighting to be done, the scientists could help out in medical or operations if they're not actively researching, etc. You could use a janitor or two also. That ship doesn't clean itself yet. Also, one doctor, one nurse and a couple of medical technicans would be more than enough for a ship of 80 or so people.
FJ - Class I Heavy Cruiser - Constitution Class: Officers (Command) - 43 Crew (Ensign Grade ) - 387 I believe GR had said everyone on the Enterprise was an officer.
He said a lot of things that never made it to the screen. TOS had crewmen of various classes as did the shows that followed.
He'd get more screen time that way. He could even end up as a popular running gag like the Chef or Morn despite never getting a line.
Here's the crew manning scheme I came up with for a Starfleet vessel of a similar size to the NX-01. Now, this was set in the late TOS-Movie era, and assums a bit more automation than we see with NX-01 (i.e. no chef, the food comes from the wall-slots, etc.). Anyway, I think this could be modified to suit the needs of the OP quite easily, and anyone inclined should feel free to do so. I hope this is helpful.
Here is the breakdown of the crew for my fanfic, Silverfin. As a cutter she has no need for a science staff, so most of the crew are operational based. Out of 126 crew members onboard there are just 22 officers. http://www.trekbbs.com/showthread.php?t=173452
When figuring out how many officers you're going to have (or need), try using this ... Officers are managers. NCOs are supervisors. Enlisted (below NCO) are the people who actually get things done and fix things.
One thing to consider here is that Archer's crew breakdown probably isn't particularly representative of what Starfleet intended an NX class ship to have. After all, Archer left for his initial mission in a hurry, intending only to shuttle a Klingon prisoner/patient/passenger to the Klingon homeworld and then to return. We know he essentially left his main armament on the pier, and only had parts of it installed in "Silent Enemy". Events just conspired to keep Archer from returning to homeport for the next two years, so he had to do with the eighty people that had boarded the ship from the intended milk run. Archer's second mission in turn involved special arrangements such as MACO rather that Starfleet ground-fighting teams, and could once again be interpreted as running contrary to most Starfleet ideas on NX class crewing. Comparing with the only slightly larger TOS hero ship, eighty is probably on the low side for the ideal crew complement; quite possibly Archer's crew isn't officer-heavy, but enlisted-light. He's got all the officers he needs, but those officers don't have the petty officers and crew they would usually employ in executing their decisions. Thus, Reed has a very hands-on approach to weapons maintenance, and when he gets help, it's from fellow officers rather than dedicated gunners and mechanics. Timo Saloniemi
I don't remember seeing any shared quarters on the NX, everyone seemed to have his own private stateroom. With double bunking in some areas of the ship, Enterprise could possibly carry 125 or more.
Also, there were spare cabins originally: Hoshi Sato was allowed to change quarters on a whim... Plus, we never saw how enlisteds should be accommodated in the ENT or TOS era. Quite possibly, they'd be stacked in bunk beds three high, just as in the TOS movie era, and NX-01 could accommodate some three hundred people in her bigger-than-NCC-1701 saucer. Timo Saloniemi
If you're referring to the time she changed quarters because the stars were "going the wrong way", the quarters she wanted were occupied by someone else, and Archer approved it as long as both parties agreed. This seemed rather unbelievable to me (though I have no military experience), because it sounds like she can't tell her right from her left, or gets confused easily when making a 180 degree turn.
Daniels shared quarters. In Cold Front, Archer is in his cabin and he (Daniels) is picking up his roommate's socks and lamenting that the roommate is a bit of a slob. No word on what happened to his roommate when he (Daniels) left and those quarters were locked. I believe there's also a reference somewhere to Mayweather sharing quarters, but I don't recall the specifics.
Dang. I watched all the episodes earlier this year, and my 6-decades old brain is already losing information. Though I did wonder if Daniels just made up that story about having a cabinmate.