Re: Miller stability
The short answer to your question is yes, you are good.
The longer answer is that the Miller stability formula is an improved method over the Greenhill formula to calculate gyroscopic stability. Any value over 1.0 is technically supposed to be stable, but in reality you want the Miller value to be 1.4 or greater to account for various sources of error. You need to spin any projectile that is not fin stabilized if you don't want it to tumble. Shape does affect gyro stability, in that a short fat bullet is stabilizes at a slower spin rate than does a long skinny bullet. The stability factor formula does account somewhat for shape by using diameter, length and mass and the differences in ogive profiles shouldn't be significant with respect to stability among the commonly utilized rifle bullets. There are atmospheric and velocity corrections to the basic formula that I would assume Ballistic makes...you could change the velocity and atmospherics to see if the Miller value changes to be sure.
You can disregard the differences in rifling contact area on the bullet. Mathematically the formula assumes the bullet is spinning at the muzzle at the rate imparted by the rifle twist with no slippage...while this may not be totally true this is close enough.
You have a misunderstanding about the velocity affect. It may be counter-intuitive but the gyroscopic stability of the bullet it actually at its least right at the muzzle. This is because for two identical projectiles spinning at the same rate, the one with the higher velocity has more force acting on it trying to turn the bullet over in flight. For our purposes, when we fire a bullet and it goes downrange both the forward velocity and the rotational velocity (or spin) will decrease. However, the forward velocity will decrease much faster than the spin, so the stability factor actually increases...the bullet will get MORE gyroscopically stable during the time of flight, not less. Why then do bullets sometimes tumble at long range? Well, there are dynamic stability forces that have overcome the gyroscopic stabilizing force as the bullet goes trans-sonic then sub-sonic. You are not likely to change those forces very much by using more spin, so a tighter twist is not real likely to prevent a bullet from tumbling <span style="font-style: italic">at range</span>.
For two different <span style="font-style: italic">muzzle</span> velocities and all other things being equal, the higher muzzle velocity will impart higher gyroscopic stability, but a change in muzzle velocity does not drastically change the stability like you might think. To demonstrate this, go to Ballistic and compare Miller values for two different reasonable velocities and two different reasonable twist rates. The twist of the rifling has a much more pronounced effect. That is why it is difficult to correct an inappropriately slow twist for a given bullet and cartridge by jacking up the velocity...you usually cannot get there before you run out of case capacity.
If you like esoteric discussions like this then buy Bryan Litz's book:
Applied Ballistics For Long Range Shooting
