On a $1,200 budget I would buy a Weatherby Weatherguard and bed the barreled action in a McMillan Hunter stock.
I did this with a Vanguard2 and it made a really good rifle great. It isn't a light mountain rifle, but it would be a prime candidate for use within the parameters that you set; "Shoot it at my range. Maybe use it for coyote hunting. Likely make it into my truck gun for opportunities than come up while rolling in the woods...😎".
I have 6.5 Creedmoors from Howa, Marlin/Savage, Remington, Ruger, Savage, and Weatherby.
