Sounds like Vapodog has offered some really good advise. You might also consider adding Ruger' s relatively new 77 Compact in SS and laminated stock. It' s barrel length is only 16.5" I believe making it the shortest of the four models. (You actually give up very little ballistically in the .308 Winchester with the shorter barrel.)

If you feel that the .308 Winchester is a little lighter than you want to consider for Elk, (though it makes a fairly good mid range Elk cartridge with a " good" bullet), then you could consider any of the three models Vapodog suggested in one of the newer Short Magnums. Be forewarned though that recoil goes up exponentially with these cartridges in the really light little guns. If you think the recoil might be a problem....stick with the .308 Winchester!

Good luck!