I get your thinking, but, alas, what you propose doesn't work except by accident. First, the Barnes bullet is harder than a jacketed bullet. Harder means the pressure will be a bit higher as the bullet goes into the lands of the rifling, and that will change the powder burn characteristic making it tend to peak higher and sooner. Even where that pressure difference isn't enough to cause a safety issue, it will shorten the barrel time of the bullet, and that will change the relationship between muzzle exit and barrel "vibration". It can walk you right off a sweet spot.
There is a reason you lower your powder charge at least 5% and work back up while watching for pressure signs
any time you change a component, and that includes changing bullets. Even if their weight is the same, their hardness and exact diameter and bearing surface lengths often are not, so they don't work with the powder charge identically.
That brings up the second problem, which is the Barnes bullet is less dense than jacketed bullets. That means it will be longer than a similarly shaped jacketed bullet. The greater length causes two issues:
First, if you use the same COL as for a same-weight jacketed counterpart, the base is sticking deeper into the case. That subtracts from the powder space, which raises pressure even before you try to get this harder bullet into the throat.
Second, greater length will make the bullet less stable for a given rifling twist rate. If your .30-06 has the usual 10" twist, you've got plenty of spin for the Barnes TSX, but you need to be aware it will take longer to go to sleep than the shorter same-weight jacketed bullet. This will make it harder to get a good group at short ranges, like 100 yards, but it may compare very favorably at 300 yards.
In general, for short range precision, coaxiality (low measured bullet runout) of the finished cartridges and optimum seating depth will be more important to getting the long, lower density bullet to do well. Unfortunately, there is no substitute for testing with your actual bullet that will get your actual bullet to shoot well other than by felicity.
Regarding measuring seating depths, there are a number of methods. You can get considerable convenience using the Hornady LNL Overall Gage with a caliper, but it's not a requirement. To start out without one, remove the rifle bolt and push a bullet into the throat of the rifle with your finger, or push it in with the eraser end of a pencil. Hold it in place while, from the muzzle end, you insert a 1/4" wood dowel in until it lightly finds the tip of the bullet. Mark the dowel flush with the muzzle. (Many use a pencil, but a single-edge razor blade flush with the muzzle is more precise.)
Next, repeat the above using a loaded round at your usual seating depth that you push in with your finger. Mark the dowel again. The space between the two marks is how much seating depth you have to play with.
If you seat out to actually touch the lands (assuming your freebore isn't too long to let you do that), your powder charge will need to be about 10% lower because of the pressure increase that causes. Pressure gets higher either when a bullet is too deep or when it gets too near the lands, so finding best seating depth should be done with a low charge first, then adjust the charge up for best accuracy later.
Read the Berger letter posted by Tang, here
. It is talking about finding best seating depths for Berger VLD's, but the basic principles apply to other bullets. That good seating depth "band" is shorter with shorter, non-VLD nose forms, but it doesn't typically have to be to the nearest 0.005" unless you are pretty near the throat.
Standard seating dies all have 14 threads per inch, so they move 0.071" per turn. 0.005" is about 1/14 of that or about 25°. Turn it in that much to get 0.005" of change.
In general, when adjusting the die body:
Angle of rotation in degrees = 360 × 14 × desired adjustment in inches
If you want to move a bullet in 20 thousandths, then:
360 × 14 × 0.020 = 100 degrees
Remember that 360 × 15 = 5040 to shorten the calculation to:
5040 × 0.020 = 100.8 exactly or about 100 degrees, or over a 1/4 turn but less than 1/3 turn.
If you want the fraction of a turn, then use:
1 / (Desired Change × 14) = Fraction Denominator of Turn.
Close enough is:
0.071 / Desired change = Fraction Denominator of Turn
0.071 / 0.020 = 3.55, so the turn fraction is 1/3.55. Between 1/3 and 1/4. Very close to 2/7, but between 1/3 and 1/4 is probably as close as your eye will estimate.
If your chamber's throat is very long, seating out to best accuracy may be too long for feeding from your magazine. Assuming you want magazine feed, set the round to the normal length, or with the seating depth so that the bearing surface is about 1 caliber into the neck, whichever is shorter. Work up the powder charge to best accuracy, then try moving the bullet in and out in steps of 0.020" to see if you find anything better, short of jamming up the magazine. If you do, re-tweak the powder charge when you get there. I don't think you'll find that the seating depth precision level is sensitive to 0.005" changes when you are that far from the throat, but you can try playing with it if you want to expend the ammunition.
Another factor with a long throat that affects performance is cartridge concentricity. If you spin the cartridge case, the bullet will usually wobble a little because the neck isn't quite straight or the bullet is tipped slightly. An old study in the NRA Handloading book showed a .30-06 getting up to an moa of group growth due to initial bullet tilt. Getting it below about 0.002" runout was the key. There are several commercial tools (Forster, Hornady, RCBS, Sinclair) for measuring this with a dial indicator. The Hornady tool includes a thumb screw for correcting it, though you can just drill a bullet size hole in your bench and learn to correct it by feel and re-measuring.
There are also special competition seating dies made by Redding and Forster with full-length sliding sleeves that tend to get bullets to seat straighter in the first place (other brands, too, but they don't seem to work as well). The Redding and Forster competition seating dies are available with micrometer depth adjustment thimbles which eliminate having to turn the die body. Choose your poison.