Just trying to keep myself straight here but, we have to remember that frequency and amplitude are two separate things. Increasing powder charge doesn't change frequency but does change amplitude. Think of hitting something with a bigger hammer. Powder charge also changes how long the bullet is in the bbl. Remember, we've done nothing to change frequency. Frequency is just a fancy word for time between nodes. For all intents and purposes, frequency is a constant at this point.
Now we get to tuners. They work just the opposite. Forget about amplitude for a minute, it later becomes a "constant". But by means of moving the tuner, you manipulate frequency and frequency is the main factor here when we're talking about timing bbl position with bullet exit.
The biggest part that amplitude plays in tuning is that more amplitude at the bbl translates to bigger groups at the target..when NOT in tune. That sounds like a bad thing but I like it because it tells me more clearly that the gun is or isn't tuned...on target. A short, stiff barrel is harder to see tune with than a less stiff bbl. I think this is what you are getting at with sporters showing more amplitude. That is correct but carries it a bit further than I'm comfortable with. In really good conditions, it's not hard to tune either, but when the wind and reality of shooting competitively come into play, I prefer a barrel that "talks to me" more clearly.
Case in point, I've moved mostly to my own contour that is simlar to a LV and away from stiffer barrels. Stiffer barrels are good in other areas and for different reasons, but as far as reading tune in the real world, I prefer a little less stiffness. That's amplitude.
Now, the benefit of amplitude beyond all that is that the arc is taller but remember, the nodes are frequency dependent. So, we have the same frequency(time between nodes) yet a taller arc, per se. That's how amplitude actually widens the tune window. Now remember, we have the same time between nodes(frequency) but a taller sine wave(amplitude)..So the barrel is spending more time where we want it and less time where we don't, because the speed at the "scatter node", which is technically the node(that's a different discussion). Suffice it to say that we want bullet exit at top or bottom, not in the middle.
Since the frequency is the same but the arc is taller, it spends more "slow time" at top and bottom but less"fast time" traversing the out of tune area. I hope that makes sense to you..or somebody.