I would add ditto on the stock upgrade as well, but I really would bed the savage. They come with pillars, and I believe anything with pillars really should be bedded to prevent from rocking on the pillars. Also remember that if you stick with the factory stock be very careful shooting with bipods. I know you said that the barrel has 1/16th clearance from the stock, but if you shoot with bipods and downward pressure + recoil could cause the stock to flex into the barrel. I'm not saying it can't be done, I'm just saying be aware that there has been issues with that.
Almost every savage I've seen out of the box will shoot 1 moa or better. I still think It's better to bed, especially with the recoil of a .270 on the pillars.
I do agree on the scope choice. My 10 power gets awful tough to shoot out that far. I also agree with incrementalism. I disagree on the gunsmith. Get a good scope and properly mount it. Then shoot it and see how it does. If that is not accurate enough then try bedding the action, I would bet money it cuts your group in half.
There is not much a gunsmith can do for the rifle, unless you want him to break it down, true the action, crown the barrel, lap the bolt, tighten the headspace to near minimum tolerance... He can't just twist a nut or turn a bolt and make it shoot better. The action/bolt/barrel combo is plenty accurate out of the box. The only thing a gunsmith may could do within a reasonable price that would help you is recrown the muzzle... IF it is already dinged up. If it's not then there is no need to crown it. I would save the gunsmith to much later, when you want the rifle to shoot .2 moa.
Edit: forgot to add. Many sporter weight barrels will shoot .5 moa. The first 3 shoots. Then the next 3 will be 1 moa. Then worse and worse as you shoot more. That sporter thats on it will be accurate for a few shots at a time. No big deal picking off yotes. The problem is... you have to actually shoot the rifle in practice to be effective in play. I day at the range shooting just 2 boxes of rounds accurately will involve a lot of down time waiting for the barrel to cool with that sporter weight. It's up to you... it can be done as is but you may want to save up for a heavy barrel.