I am going to concur with much of what has been said.
Multi-purpose rifles means you are making significant compromises somewhere.
For a long range Elk rifle, the .300 Norma Mag would be hard to beat, though there is much to be said for the tried and true .300 WM and 7RM. It depends on your definition of long range.
For paper punching, the 6.5 CM is hard to beat.
Keep in mind, these cartridges are hard on barrels, even the 6.5 burns throats significantly faster that the good old .308.
This will require regular barrel swaps (depending on the number of rounds shot).
Keep in mind, just because you have a rifle and scope combo capable of making an 800 yard shot on an elk, this doesn't mean YOU are capable of making a 800 yard shot on an elk.
My suggestion is this:
Build a training/paper punching rifle and a dedicated long range hunting rifle.
This can be done while still falling into your price bracket.
For example, you can buy a Shilen rifle for 3500-3800 dollars.
Equip both rifles with the same stock, same trigger option, same magazine option.
If you ended up with rifles at the top of the price list, 3800, that is 7600 dollars.
This leaves you 2400 dollars for one excellent scope and rings,
Or, you could outfit each with the very good DMR II, which would put you a few hundred over the 10,000 limit.
Chamber your trainer in .308 for very long barrel life, relatively cheap components and ease of shooting. Shoot, shoot and shoot some more.
The Shilen action is made by Stiller, they are very nice actions. Shilen barrels are very good, their triggers are pretty awesome.
You could order barreled actions only and stock both rifles with Grayboe stocks (very nice stocks) and save a few hundred.