Think of it from the other side.

Who cares what the tuner is doing...

If it works it’s because the tuner has moved a certain amount of weight toward or away from the receiver

Nothing more nothing less.

Leave the blacks magic out if it and possibly focus on that we know for sure.

Ex

A particular barrel might need the tuner moved farther out than another barrel of similar proportions.

But as long as the tuner has the weight and the correctly sized adjustments the tuner will work in that component/barrel criteria.

Shooting a truck axel barrel will need a much heavier tuner than a pencil thin hunter.

That tuner weight and it’s adjustment is just a percentage of barrel strength/flexibility.

What you're talking about is a moment force to cross sectional area ratio with a factor for barrel material thrown in. Longer barrel and heavier tuner means a larger moment on the barrel. Divide that by the (average?) cross sectional area of the barrel.

It may give a useful number and it may not. We know all those variables are related, but we (or at least I) don't know how they are related exactly. The ratio method as I described above assumes a linear or inversely linear relationship between all the variables. That could be true, but some of those variables could be raised to a power, rooted, or have a modifying factor.

For example, maybe the barrel contour matters much more than the weight of the tuner, so the cross sectional area should be squared, or the weight of the tuner should be multiplied by a half because that's what the data shows.

I see your point, the only thing I'm getting at is that we don't know the exact relationship between all these variables, just a starting guess. It would take a lot of different barrels, tuners, and ammo to test all that and come up with a sound relation equation, unless one already exists that I'm not aware of.