I'm very sorry to see this thread die in the usual way. Perhaps after nearly two year's rest my little nudge can move it forward?
First of all, I'd like to address in my own way some of the questions asked by 45 2.1. Why do I think I am where I am and not doing better? Because I haven't mastered the launch....specifically the first half-inch of bullet travel, in every one of my rifles. With some I have come close, based on results, but many still challenge me. Working out powder type, the necessities (and non-criticals) of case preparation, general fitness of the rifle, bullet lube, and a few other details such as working with the vibrations of the rifle and shooting/resting positions are relatively easy, but job number one with fixed ammunition is to get the bullet into the bore with its center of form concentric with its center of mass, and that seems to be the rub with myself and almost everyone attempting to improve accuracy.
Two-diameter bullets fail on several levels. The first is that they are woefully under-supported by the interior of the barrel when fired. The "bore-riding" noses depend upon the tops of the lands to keep the nose centered in the barrel, and that supporting surface area is very, very small when considering the form of almost any modern rifle barrel having very wide grooves and narrow lands. Once the forces which always try to turn the bullet any way but straight exceed the ability of the alloy to resist, the lands will sink into the bullet nose and allow the nose to turn into the side of the barrel...thus it won't "come out the muzzle straight" as someone mentioned previously. I have recovered numerous bullets whose bore-diameter noses have turned to the limit of groove depth on one side only, scarcely having touched the land on the opposite side, and they did not shoot well. The second failure mode of a two-diameter bullet is in the rifle's tapered throat, where due to the dissonance of shapes there is very little of the cylindrical "body diameter" of the bullet actually being supported by the throat when it is fired, so the bullet easily collapses into one side or the other of the throat rather than swaging straight into it. A cylinder being forced into a conical orifice will tend to gimble, not a condition conducive to getting the bullet into the bore straight. Some will say that wide grooves, such as two-groove Springfield '03s or even the nearly equal groove-land ratio of some rifles like the military Swedish Mausers, will better support a bore-riding nose, and that may be the case at moderate velocities when using very hard alloy, but it is most certainly NOT the case when one attempts to push near the jacketed bullet velocities for the cartridge. One reason wider lands do not solve the problem of keeping the bullet straight at high velocity is that wider lands create more stress on the driving portion of the bullet by requiring more metal to be displaced than narrower lands would. Reducing the stresses of jacket deformation is why narrower lands have become the standard, and the cast bullet is no different....maybe even more critically affected by wide lands because the diameter is typically larger to fully obturate the bore against gas loss. More metal displaced = more engraving resistance = more powder gas force on the base.....which = distortion (riveting and/or bending of the part of the bullet not yet safely moved into the parallel portion of the barrel where it can be fully supported). I worked for several years on a theory that bringing loaded chamber neck clearance to near zero, and in one case actually zero, would cure all the ills of crooked bullet starts into the throat, but for reasons which still elude me it never proved to be the full answer to alignment in my own testing.
For my purposes at least, cone-in-cone doesn't work very well either, except when there is adequate room for alloy to displace in a uniform manner, and the bullet is contained almost entirely in the throat (just the gas check in the case mouth and a minimum of nose protruding past the throat to only be supported by the tops of the lands. This method of fitment is impossible in most instances without modifying the rifle's throat to a form it won't maintain anyway as it wears. A Loverin-style bullet, with multiple, narrow driving bands, usually stair-stepped into a crude taper from bore diameter to throat entrance diameter or larger can shoot very well, but typically lack the necessary bearing surface to withstand the forces of being launched at near full-potential velocities for the cartridge...they erode, leak gas, and accuracy suffers. Conical, smooth bullet noses can actually work extremely well in rifles having new throats composed of a series of parallel portions and abrupt tapers, such as in a typical .308 Winchester chamber, provided the forward-most full bearing surface is carefully sized to closely fit the freebore diameter. I think there's a lesson to be learned there.
Much of my interest involves getting the nearest to jacketed bullet velocities as I can from cast bullets, in "rifles I'd carry in the field to hunt with". I do not compete for absolute minimum group size, but I do consider ten shots into one minute-of-angle to be minimum acceptable, and I require bullets be made of an alloy suitable for humanely killing game at the velocities I am able to achieve. Others may desire the smallest groups for paper or steel with all else being secondary.
So this brings me to a question identical to one asked more recently on another thread in this section, the answer to which I believe will greatly improve my shooting and anyone else's: How do we fit a bullet to a rifle in such way that it has the highest tendency to go straight? I have had the most success in worn rifles using bullets that have three principle attributes: Very little unsupported nose length, a series of tapers which generally match, but DO NOT exactly mimic the shape of the rifle's throat, and driving bands which are neither too narrow to handle the rifling torque without leaking on the trailing edge nor too wide to easily deform without causing undue stress/deformation of the rearmost portion of the bullet before it is safely pushed into the throat. I believe that a slight mis-match of bullet nose angles to throat angles, allowing a gradual rather than abrupt increase in engraving resistance, is key to getting a bullet straight into the barrel, but do not fully understand exactly where contact needs to happen first and last to best align the bullet dynamically. Any specific input on that would be greatly appreciated.