I'd like to see some of the good traits of BSG integrated into Trek, sure. But I wouldn't want to see a reboot of Trek that artificially forced it into being a BSG clone. But yeah, I'd love to see the caliber of writing (miniseries - season 3) that BSG had, along with:
1) a slightly more formal military attitude in Trek
2) a wide and varied cast of interesting supporting characters
3) main characters that have a great deal of complexity
4) arching stories
Yes to all of this plus - more women.
You could certainly set the show during a war but not have the entire series be set around that war. A 5-year mission is definitely more fun.
Personally, I thought Nu BSG missed a trick. A whole season set on Carillon with a modern take on the ovions (and Cassiopeia!) would have been great fun.