I am going to come at it from another angle. Find a used 700 ADL or BDL for under four hundred and look at gun shows or online for a good used leupold scope. Throw in some forty dollar leupold mounts and you should be around seven bills or so. Its not going to be a Cadillac setup but it will be a Jeep and get you where you want to go.
That will get you a .308 that will shoot as good as you can. Or buy a .243 or .260 or 7mm-08 if you find that. Then take the seven hundred and change left over and find a used 7 or 300 mags in a rem 700 mountain rifle for the Elk hunting. That would be my route.