For the bullet I would have the indicator out nearer to the bullet tip. That will maximize the sensitivity of the reading. In the same way I think you'll find putting it just behind the case mouth will maximize case neck runout sensitivity.
The case neck runout is what is limiting how close to perfect your final result gets. I find the spherical carbide expanders available for Redding FL dies pull necks off less than conventional expanders shapes do (and use neck lube despite the carbide to have even less pull), but the least runout of the neck can be had by eliminating the expander altogether. To do that use either a bushing die with the right size bushing to bring the neck ID down to the same size the expander would have left it, or use a Lee Collet Die
for the neck and separately set the shoulder back in a Redding body die (the body die doesn't touch the neck).
Yep, no mystery why improved alignment results in lower drag. You still have the epicyclic motions (coning, nutation) introduced by the bullet tip realigning from coaxial with the bore over to the yaw of repose for flight down range, but once it settles into the new equilibrium, it's clear sailing to the target.
As to why the bullet in the throat trick didn't work consistently with Berger's VLD's, I don't really know any more than I know why it doesn't always work with some other bullets. Dan Hackett had an example in the Precision Shooting Reloading Guide of a 50 grain Nosler bullet in a 220 Swift that would not shoot five rounds into better than 3/8" at 100 yards when seated 0.020" off the lands (his presumed magic number). But when he accidentally turned his seater micrometer adjustment the wrong way and loaded 20 round to 0.050" off the lands, those 20 rounds gave him two 1/4" groups and two bugholes in the 1's. I do know Berger found tangent ogives (most Sierra MK's, though not the newer 125 grain .308 MK) self-center better than secant ogives (their VLD shapes), so Berger now has a "hybrid" ogive that starts out tangent then becomes secant after it's below bore diameter. That's to try to get the best of both worlds.
As to why different amounts of jump with the same bullet are best in different chambers, I don't know the reason for that, either, but my imagination has arrived at one theory for which I need to develop some hypotheses to test. It has to do with gas bypass around the bullet at firing. In the old Dr. Lloyd Brownell study from 1965 at the U. of Michigan, he suggests the reason pressure from a given powder charge drops as you increase bullet jump away from throat contact is that more gas then allowed to bypass the bullet before it obturates the bore, thus slowing pressure rise and lowering start pressure. Of course, if you seat the bullet too deeply and start to subtract too much from the powder space, pressure starts to rise again, despite the addition gas bypass opportunity.
Below is a plot from Brownell's data, with pressure adjusted down 20% based on Harold Vaughn's estimate of calibration error introduced by Brownell's use of the infinite cylinder Lamé Theorem for hoop stress on what was not an infinite cylinder, but the chamber end of an '03 barrel.
What my vivid imagination suggests is that bypassing gas in the right velocity and pressure range can form a gas cushion around the bullet, allowing it to self-center. Too much gas bypass and you have buffeting turbulence and a cocked bullet. Too little and you have no effective gas bearing. You can create both situations by propelling a bullet in a loose fitting tube with compressed air at different velocities, though it's easier to to with the bullet nose facing into the gas flow.
When you have the bullet in contact with the lands and no significant gas bypass occurs, you get good nose alignment but the back end of the bullet can still be tipped. Uneven radial expansion of the brass, as Stubbicat described, could throw the bullet base toward one side before the neck expands far enough forward to center it. The longer the bullet the more leverage any back end tilt has to pull the nose off-axis in the throat. Hence, part of the reason for greater problems in some rifles with VLD shapes. The other part is the greater angle of departure of a secant ogive from the bullet bearing surface won't resist being pulled off axis in the throat as firmly as a jammed tangent ogives does.
The end result, particularly for long VLD shapes, is a need to combine throat contact with tight control of the alignment of the back end of the bullet. One way is a custom chamber for tight-fitting outside-turned necks. I think that mechanical alignment likely accounts for the relative insensitivity of many custom benchrest and varmint guns to neck and bullet tilt and even to banana-shaped cases. For a looser commercial chamber neck, though, you need all the help you can get, whether from a gas cushion, perfect case wall uniformity, etc.
Of course, I may be completely full of beans with the gas cushion idea. I need to get a set of "if it's true, the observed effect will be" hypotheses to test. In the meanwhile, I know quite a number of folks have reported finding what seem to be two sweet spots in bullet seating depths in their guns. One close to or right in the lands, and the other with the bullet further back where my theoretical gas cushion may present itself optimally. The problem with these anecdotal reports is getting variables isolated. Changing seating depth changes pressure which changes velocity and barrel time, and so what people think is a corrected seating depth may actually be better adjusted coordination of barrel time and muzzle position "vibration". It's a great and complicated mess of possibilities, as always.
"First contemplation of the problems of Interior Ballistics gives the impression that they should yield rather easily to relatively simple methods of analysis. Further study shows the subject to be of almost unbelievable complexity." Homer Powley