Bart,
(warning, long discussion including basic trigonometry. Stop reading now if this offends you).
I've never taken high speed photography of a barrel and I've never calculated the natural frequency of a 30" HV barrel, but it wouldn't be too hard and I'm sure it has been done. But I have a lot of experience with harmonic oscillators and some experimental data using Mike Ezell's tuners so I'll post what I think I understand.
If every round was the same, then tuning wouldn't do anything. It wouldn't matter where the muzzle is or what motion it is in since it would be the same for every shot. But rounds aren't identical. So what you want to do is minimize movement of the muzzle at exit. Most people would think you want the muzzle at neutral, pointed straight, but that is actually when it is moving the fastest. It has to stop at each extremity as it changes direction and that is when it is moving the slowest. You also don't know what plane it is vibrating in, up and down or left and right, or a combination of the 2. Lets use up and down for this discussion.
As you tune the load, by moving the weight .001" per group, you find a place where the groups get better within .005" in my experience (each mark on the Ezell tuner is .001"). Now all you know is that it is better grouped. So you don't know if you're at 180 or at 360 (up or down). You can keep going another .005" and see which node makes a better group. But I don't. I stop and call it good.
As an aside, the sine wave I used in my previous post is actually a cosine wave since cos 0=cos 360 =1, cos 180 = -1. Both of these extremes represent the stopping of the barrel as it reverses direction. Also, if you look at the cosine wave, you see it gets almost flat for a while near the top. That is the best place to tune to. Of course we do it experimentally so you don't really know where you are, just that the groups are smaller.
So in summary, as I understand it, the 180 and the 360 should be the same for tuning.
As for how much it takes to tune, I know from experience it only takes a few .001's of an inch with ezell tuners. I use big brakes (if a little brake will do it, then I just forgo a brake) that weigh similar to the ezell tuner so I'm thinking .005 to .010 will take you at least to the nearest node.
--jerry