How much are you going to spend on a barrel, stock, smithing, shipping, etc? Yes you can buy a whole rifle, but you'll probably only get $50-$100 for the stock and factory barrel.
Will it cost more than just getting a Savage 10FP or an 10FP HS Precision? Most likely. What are you going to do at 600 yards? F-Class? Why not just get the 12 F/TR from the get go? If it's just a range rifle and you'll never compete with it, the the 10FP will do fine.
That said I'm totally in love with my custom barrel, but it adds up quick. I did a "custom" rifle on the cheap last year. All told it cost me ~$800 using a new Model 11 FNCS as a donor; it will shoot 1/2" groups and is a breeze to clean. (I kept the factory stock and I'm holding on to the factory barrel just in case I ever get to hunt out west.) You can easily get a 10FP for that.
If I were building a 600 yard rifle I would forget about a Stevens action on just order up a Savage Target Action for ~$600, but then once you add a barrel and a stock you might be better off ordering up a 12 F/TR.
I'm not trying to ruin your fun, I'm just looking at all the angles.