Most "turkey" shotguns have the short barrels for the reasons you listed, ease of carry and swinging to get a shot on a turkey. If you look into a short barreled variety, look at either Turkey Creek chokes or Patternmaster chokes. Then check out Hevi-Shot, Magnum Blend. Its expensive, but it is DEVASTATING on turkeys. If you go with a 26-28" barrel, I would still check out Hevi-Shot, but run a full choke instead.
I hunt with a 26" barrel, full choke and Hevi-Shot #5's. I killed 4 turkeys last spring. 8yds, 38yds, 56yd and 70yds. The 70yd bird was pushing it, but I misjudged the distance. Found out after I went and picked the turkey up. I do feel confident to kill a turkey, for sure, at 65yds with this combo.