Advice Sought - New Elk Rifle

I would not choose 308 over 7HT(7-08) except in this circumstance: if I want to shoot buckets of cheap surplus ammo.

A .308 with a 150gr monolithic bullet or 165gr bonded/premium bullet would be the ticket, I'd think. The 6.5 CM has a tremendous following for good reason, but a lot of it is marketing, and a lot of the benefits are at longer range, which has already been covered above. The .308 in a lightweight package will buck pretty good, but if you're used to your 7mm Mag, it shouldn't be a problem. The beauty of the situation is that you can't make a wrong choice here. 6.5CM, 7mm-08, or .308 will fit the bill nicely for what you're asking.
As far as the platform itself, Tikka, Howa, Bergara, and Savage all have tremendous factory offerings that are all around the same price point, so if I were you, I would go in and see which feels best. I suspect that since you already have a Tikka, that platform will feel the most familiar to you, which will aid in muscle memory for when the shot presents itself.