People all too often get too high of a magnification on a scope, ESPECIALLY when going after big game. 4X for a 275 yard shot is in no way "under-powered" on the scope. Been there, done that. I've never made an initial shot under 200 yards for elk here in Utah. Deer are closer, but can also "be out there".
1. The famous 3-9 is famous simply because it is so good at matching up with what's needed. I've never cranked a scope above 6X for a hunting shot.
2. 40mm optics are as large as I'd get, simply because it'd raise your sight picture off of the stock. 40mm glass with low mounts.
My suggestions? 3-9X40, 3.5-10X40, or 4-12X40 scopes. Partial to Leupold. VX-II or Vari-X III.
Mark in Utah