Were it me -- and I have been there, with a muzzle heavy rifle -- I'd put the 13 ounces back in the butt -- or a bit more if you can use a lighter scope -- and shoot it. 3/4 of a pound right at the end of the butt can do a lot to rebalance a rifle.
Adding width in the front will make the rifle more muzzle heavy -- whatever weight is involved in adding those rails, and width, is all weight in the wrong spot. The extra width can help with torque effect, but that only begins to appear with .30s and heavy bullets.
I remember Charles Bailey's light gun. Somehow 'ol CB won IBS Shooter of the Year with his heavy gun only -- his LG never would shoot. .300 Ackley, as I remember. Then he took the extra width and rails OFF his LG, and it started to shoot. Fortunately, he then moved, or none of us would have won anything. (Unfortunately, he's a good guy and we miss him.)
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As I'm sure you know, moving the front rest out on the forearm also helps to rebalance the "shooting" of a muzzle-heavy rifle, but you do have to allow for recoil. Having the rifle slide off the front rest does nothing good.
As I remember, 410-R stainless weighs about .252 pounds per cubic inch. I'd check that number -- my memory isn't what it was when I was a mere child of 50. Getting a pound out by fluting then, requires removing about 4 cubic inches.
There have been some claims that removing any metal from a barrel, either by fluting or re-profiling it -- will cause the diameter to open up a few .0001s. But others say if the barrel has been properly stress-relieved, that won't happen. My take on this is "I don't know," so to be a bit safer, I'd not flute the last four inches of the barrel. That way, even if the barrel grew, there would be a bit of choke at the muzzle. As long as it doesn't have any choke now, that would be more apt to help than hurt.
Remember too that current thinking on "tuning" a barrel has to do with harmonics and vibration, esp. the third order harmonic. Changing the mass or profile of the barrel will likely change the "tuning" point. Whether or not you'd occasionally run into a barrel where reprofiling (or fluting) would move the "tune point" to too high pressure, or too low velocity, I don't know. But usually the best solution to that one is to add weight to the muzzle -- about 4 ounces will usually do the trick. And that's just what you can't do.
So, if this is a hummer barrel -- where "hummer" means one that for some reason shoots through wind changes better than it should, I'd leave it alone. In fact, I'd take it off & save it for National-level competitions. I'd lighten the stock, whatever it took, to rebalance. Those barrels don't come along very often.
If it's just a very good barrel, well, those are more common.
FWIW
