Dan,
If you are looking for a manufactured rifle in your price range you can not go wrong with a Sako 85 or TRG. I own a couple Sakos in 300WM and 375H&H and both shoot 1/2 moa. The 375 is my Alaska and Africa gun. The 300 we shoot long range with on a regular bases, out passed 1000 yards. Running 215/220 bergers in the 2800fps range it rarely misses and is supersonic and stable enough to shoot a mile. Other than a Sako if I were going to spend upwards of 5000 I agree with others build a custom rifle. For probably closer to 4000 you could build a custom rifle on a defiance or surgeon action with a bartlein or kreiger barrel in a manners or McMillian stock or even a krg chassis with a timmney Calvin Elite trigger and shoot better than most of us could think possible. I have a few customs in 6.5 and 338. Look up Meredith rifles in Athens, Alabama. Tooder Meredith builds some of the best rifles around. If nothing else he would be worth a conversation.