Actually, in German Salazar's review
, the Redding Comp die did straighten things up a little. Targets are shown of the effect of the seating dies tested on precision. I have to point out, however, that while some gun/bullet/load technique combinations can have up to about an moa of group spread due to bullet tilt, others show almost none. You pretty much have to test to see if your particular gun and load setup is sensitive to it.
I think the best test is one Harold Vaughn devised. He intentionally tilted bullets a little over 0.2° (about 0.0035" tip tilt off-axis) in a 6 mm BR rail gun being fired in a tunnel range (no wind) and got about 3/8 moa spread by firing 8 shots, indexing the direction of the tilt 90° for each shot. The result was a 4 leaf clover, with each leaf being two holes (Rifle Accuracy Facts, H. Vaughn, Precision Shooting Pub, 2000, pp 133-134).
When A. A. Abbatiello did an 829 round test of M72 .30-06 NM ammunition in the 60's (probably an '03 based match rifle—he didn't say), he sorted with a runout gauge and got the bigger 1 moa dispersion (Handloading, NRA Books, 1981, pp 86-87). On the Shooter's Forum in the last week there's been a member posting about a .22-250 giving him 1 moa difference between straight and tilted as well.
Two factoids worth noting: Vaughn, former head aeroballistician for Sandia National Labs, used 6 DOF software with detailed information on his bullet to show the dispersion should have been 0.464 moa theoretically. It was was smaller, he surmised, because of a degree of self-straightening in the bore, calculating only two tenths of a thousandth of an inch of straightening was required to account for the difference. Indeed, he also found that if the bullets were seated closer to the lands than 0.030", the self-straightening increased, giving him a still smaller group. This likely explains why 0.020" off the lands or closer seating are frequently cited in accuracy loading, though that doesn't work all the time. Abbatiello also found a straightening effect wall, in that bullets tipped more than 0.004" off axis provided no additional group dispersion, as if any tilt beyond that degree were straightened.
The second is that both authors found you could reduce a group by orienting the tipping in the same direction for all your rounds. The double-holes in Vaughn's clover leaf are the example. Abbatiello was sorting rather than controlling tilt, but in the mix of degrees of tilt he found that if all were indexed to the same tilt (say, all tips pointing to 12:00 in the chamber) the dispersion due to tilt was halved as compared to allowing random orientation). This likely explains why you can tune self-loaders to half moa, despite the fact the forcefible feed is known to tip bullets. The bullets are tilted in the same direction.
Bottom line, test your load at your seating depth with some version of the way Vaughn did it. Drill a hole in a board or on your work bench about the size of your bullets. Stick loaded test cartridges into the hole nose-down and press the case with your thumb until you tilt the bullets enough to register about 0.008" TIR (Total Indicated Runout; the range of the indicator readings) or a little more on each bullet. (When you rotate a cartridge in the gage tool, the bullet tilt adds to the reading on one side and subtracts from it on the other, so TIR is twice the off-axis tilt; i.e., 0.008" TIR indicates 0.004" off-axis tilt). Use a Sharpie to mark the high side (or the low side, as long as it's always the same) of the tilt on the case head where you can see it looking into the back of your chamber. Collect about 20 of these. Now use the hole in the bench to straighten 20 more rounds to as close to zero runout as you can.
At the range, set up two targets. Target A for the tilted bullets, and Target B for the straight bullets. Fire up to four rounds from each box of ammo as fouling shots. Then fire alternating between targets. 16 will go into target A, indexing the bullet tilt direction 90° between shots. 16 of the straight rounds will go into Target B. Alternating causes shooting conditions variations like bore fouling, barrel temperature, lighting wind and other factors that affect the shooting to even out during the test. At the end, see if the group sizes are different on targets A and B. If A is bigger, you have tilt sensitivity in your gun and load combination. If not, you don't.