Nice restrictions. Certainly makes for an exciting... 2380.
It was damn difficult, too, but that was why I set those for myself. Shelby, Nog, Ogawa, and Dax were all easy. We didn't see Ogawa in
Insurrection or
Nemesis; with
First Contact set in 2373, I figure she could be a doctor by 2380, and we already see in an alternate reality that it was a possible future for her. For Dax, I liked the idea from the DS9 Relaunch of her moving into command, so I decided to steal that for my crew. Went with Nog simply because he amuses me, and Shelby because I'd like to see what kind of officer she would've become in the intervening years since "Best of Both Worlds" (even though I already love her in PAD's New Frontier series). The rest of the command crew was the hard part; I spent about an hour combing through old recollections via Memory Alpha to come up with that list. I also considered Melora Pazlar for Science Officer, but ultimately decided on Mendon because I was already trending far too much to humans and near-humans. I do wish I had incorporated more DS9 and VOY characters in hindsight, but I'm just not as familiar with those series at this time as I am with TNG.
Now, for another "go," without my previous personal restrictions, instead going solely with the ones set forth in the original post:
Commanding Officer: Data
Executive Officer: Kira Nerys
Tactical Officer/Security Chief: Tuvok
Chief Medical Officer: Julian Bashir
Chief Engineer: B'Elanna Torres
Science Officer: Jadzia Dax
Flight Controller: Tom Paris
Operations Manager: Nog