While, IMHO, the Forster Co-ax press is going to give you straight ammunition more easily than other presses with a wider variety of dies, I've managed to get pretty straight ammunition even off an old Lyman Spartan Turret press with the right dies. If you are careful enough, you might end up having trouble seeing any improvement over the Rock Chucker, provided it was made with good alignment and symmetrically cut die threads. Ditto the die itself. Rocky's alignment check can help with that.
Concentricity involves four things:
- case neck concentricity with the case body
- neck wall thickness uniformity
- bullet seating straightness
I would have added a straight case body, but fireforming usually takes care of most of that. You do get the occasional banana shaped case that won't straighten under pressure, and it won't read a concentric neck no matter what you do. Set the indicator between the two case supports to see that. If the annealed case doesn't shoot itself straight, then you may simply want to set those aside for plinking, load development for pressure signs, firelapping, and etcetera.
If the case neck is not concentric coming out of the sizing die, it is being pulled by lateral force. A bullet seated straight into a tilted neck will still give you cartridge runout and the bullet will not be launched straight into the bore, which is the object of the concentricity exercise. An English shooter posted recently that an article in one of their magazines had tested all available sizing dies (though this probably preceded the new Redding sliding sleeve bushing neck die design). In particular, neck sizing dies are problematic since they don't grip the sides of the case while the neck is pushed and pulled through the sizing portion of the die, so there is a lot of leverage available for pulling the neck off-axis from the base end. A second opportunity to pull the neck off axis occurs when the neck is pulled over an expander. That's even a problem for full length dies, as the case body is unsupported by the sides of the die as it is withdrawn over the expander.
The only neck sizing die they found that applied no lateral force and gave resized necks that were consistently 0.001" or better, believe it or not, was the inexpensive Lee collet die. It flat out did better than any other die. It sizes the neck by squeezing it against a mandrel. That means no expander is needed. Moreover, that mandrel prevents the formation of "the dreaded donut" on the inside of the neck and shoulder junction, so you don't have to worry about inside neck reaming cases with a long history. Despite its modest cost, it seems to be a better mouse trap in principle. The Lee die takes a little getting used to. You may find you have to anneal case necks more frequently so it gives you its best neck tension. Every three rounds is good for consistent neck tension, anyway.
Neck wall thickness matters because the conventional neck sizing dies act on the outside of the neck, tending to make the outside concentric with the case body rather than the hole, though the Lee die creates a helpful compromise in this regard. If the outside is concentric, but not the inside, then even with the hole in the neck being parallel to the case body axis and with the bullet straight in that hole, you will still have runout. Sorting your cases by neck wall runout will eliminate that component of the runout problem. So will outside neck turning if you don't mind the extra working of the brass between firing and sizing that brings about? Again, frequent annealing addresses that problem.
Finally, you've got to seat the bullet straight. With conventional dies, sometimes interrupting the seating stroke with case rotating helps, as Kdub described. Other times it doesn't. That seems to depend on how straight the neck is on the case to begin with? The Precision Shooting Reloading Guide describes using an O-ring between the press and die nut to allow the die position to flex to self-align. A fellow who tried that on this board didn't seem to get any help from it. You could try turning the seater die into position loose (no nut) and use a mark from a Sharpie to locate its vertical position on the press, then just let it float in the thread to see if that helps? Just be sure the mark is lined up as you start each bullet in.
In my experience, straight seating is one place where the right die makes a big difference. The way I got straight seating on the Lyman turret press was to use the Redding Competition Seater Die. I understand the less expensive Forster version (apparently Forster came up with the idea, originally) works as well, but I don't own one to say for sure? When I first got one of the Redding dies, I found it put a bullet into a true .30-06 case straight enough that the runout was typically half a thousandth plus the neck wall thickness variation. That is with Sierra match bullets, so YMMV with others, but it is a good starting place.
Both the Redding and Forster use sliding sleeves that line the case up, and a floating seater plunger that lines itself up with the bullet tip. I understand second hand that other brands of sliding sleeve seaters have not proven to be up to the Redding and Forster products. Apparently they are the only ones on the market that have the necessary machining precision and to have achieved the necessary full case alignment. The Forster is available with or without micrometer adjustment, so a less expensive version is available to try. The Redding is micrometer only. I like the convenience of the micrometers, but they are a luxury and not a necessity.
Finally, you can bend a crooked bullet into place. NECO makes a special all-bullet fixture for this, but you can just drill a bullet-size hole in a piece of wood. Stick the bullet end of a cartridge in and by trial and error put enough lateral force on the case to straighten it. I have no idea what, if anything, this does to neck tension. It's a lot of extra work if you can avoid it, but it should give you a chance to see how much difference concentricity makes in your rifle before investing in the different dies.