Look into building a semi custom. You may be able to put together a gun for a similar price. Unless you want the gun right away this is what I would do. Keep your eyes open on the classifieds here and on other sites and you should be able to pick up some parts. If you are lucky maybe even find a used semi custom rifle ready to go.
Barrel-$550
Action$500
Stock$3-700
BM-$200
trigger-$200
Gun Smith-$600 trueing and chambering
TOTAL=$2750 (That is with $700 budget on stock)
Add another $2-300 for a brake and having it threaded.