Andy, you are making a false assumption.
Chambering a crooked round will not straighten it. I have checked this, and it simply does not happen.
I have also fired rounds that were as much as .003 crooked, and they went into the same hole as ones that were less than .001.
We do a lot of straightening in our shop, you learn a lot about how materials act when subjected to a particular force. I have often wondered about how various round straighteners. I have always thought that there is the possibility of actually bending the bullet than moving it in the neck. ........jackie
OK, let me say right up front, I have no indispensable ego attached to anything in this reply, so have at it. I'm in learning mode.
I wondered that too. So after I straightened them, I did some checking to see how they tested. I didn't see any evidence of the bullet being bent.
I use this tool
http://trutool-equipment.com/ to straighten the rounds. My biggest problems have been with 7mmMAG though I seem to have solved part of the problem anyway. Some of them were as much as +/- 0.006" (0.012" total indicator movement). Lately they have been better, about half that, but I have no clue why.
I have some heavy aluminum angle in the shop and have thought of running a chamber reamer into it up to the base of the neck to get a better fit on the neck of the cartridge but I haven't done it yet. I also thought of trying to ream a hole that was groove diameter + 0.001" or so to bear only on the bearing surface of the bullet but discarded that idea as impractical since it would require a custom set of reamers.
I have a cut off chunk of .308 barrel blank that I could push my .30-06 reamer into with the idea of making a tool that fits the neck but I haven't done that yet either.
I was surprised at how little force to get the bullets to run within 0.002" total indicator movement. I think the Hornady tool may be a better combination if eccentricity is the only concern, but I didn't get it because it does bear on the tip of the bullet which is probably more vulnerable to distortion than the neck and the bullet body before the ogive which is where the current tool exerts force. OK, a few thousand words worth of pictures ...
This shows a dummy round in the tool from the case side. I normally pull up but the effect is the same either way. The edge of the tool bears on the neck of the cartridge close to the base of the neck.
This shows the other side of the tool. The aluminum tool bears on the bearing surface (full diameter) of the bullet just beyond the neck.
Those look to me like they might be the best places to put pressure if one is going to try to straighten the cartridge.
The case at the base of the neck is still supported by the bullet so it takes a lot of force to dent it. The body of the bullet at full diameter is pretty solid and given the low forces being used doesn't seem likely to be deformed. I don't see any deformation on straightened cartridges anyway.
Anyway, the process is dirt simple and results in what measure as much straighter cartridges than I started with. The only ammo I seem to have to use it on is .30-06 and 7mm Rem MAG. .22 Hornet, .223 and .17 Rem seem to come out straighter. .243 I sometimes use it but not often.
Fitch