I do it all the time, too..lol. I actually went and looked at mine to make sure before I posted.
I have both a 695 Mossberg and a Savage 220. While I much prefer the 220, the 695 is a shooter in its on right.
A used higher-end Savage, an older used A-Bolt (not the AB3), or you could possibly find a used X-Bolt in your price range. A used Tikka would be in your budget as well.
If you are set on new, look at the CVA Cascade or Ruger American, or even one of the other options listed in previous posts...
If you are up for a long trip before you unload, check out Windrock Mountain in Oliver Springs, TN. You can ride for days and days there. And if you are interested in a campground there, I recommend Half Moon Campground.
I sometimes wonder if the reintroduction of wolves and grizzly bears is not just a clever tactic by anti-hunters who are in DNR leadership. But I hope I am wrong.