You want to measure from where you see the grey streak from the bullet cutting the paper to the opposite gray streak on the other side of the group. You have to subtract the diameter due to dementinal size of the bullet. If you don't subtract the size of the bullet, you could never shoot a group smaller than .308" even if it was a one hole group.
"Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it.  But small is the gate and narrow the road that leads to life, and only a few find it.
If you find your self in a fair fight, your tactics suck!- Marine 1st Sergeant Jim Ryfinger
Friends don't let friends develop canonitis!-chucknbach
arguing over the internet is like the special Olympics....even if you win, you are still...special!
With a budget up to $2k, you could easily go the custom route as well I would think. I would also throw a Rem 700 Sendero into consideration too, although they don't make new ones in .308 anymore, but you can still find them new in some places like this: 700 SENDERO .308 REMINGTON for sale (951808480)
For $2K I would definitely go the custom route. A much better rifle than a factory made one. Senderos are good rifles, I have 2 that I bought used that are great shooters, but for $1650 off the shelf, you can keep them.
You will never know how much it has cost my generation to preserve your freedom. I hope you make good use of it.
~ John Quincy Adams
I have owned three Remington 700 Mildpec 308''s since they were made available as a non catalog offering, and as I understand it, have barrels that are over runs from M24 production. They were all very nicely finished, and shot sub .5MOA out of the box. Nicely balanced with a varmint weight barrel, all stainless, and an HS Precision stock with Wundhammer style tactical grip. they run around $1000-1100. They are tough to find, but I bought all three 308's, and recently a 300WM Milspec from, The Exchange. They list on Guns America. They don't always have them listed, but he gets them on a regular basis. Another good alternative to take a look at.
OP--Upgrade to the .300 WM to begin with. You'll never regret it. JMHO.