Ok, after some real life testing, I edited this post because I was wrong in a part of my logic. But things still may not be what you think they are, or have been led to believe, so read on....
I respectfully disagree, Art. I concur with what NYArrow said. "In my mind it seem three under would bring the limb around even more than split finger. I always assumed split was a more centralized form of shooting and 3 under is where the stronger bottom limb comes into play."
Here’s my thinking. The string is effectively divided into two parts of set length once the string hand is placed and begins pulling. It may help visualize this if we think of the bottom tip(left tip in Roy’s pictures) as point A, the top tip(right tip) as point B, and the hook(or fingers) on the string as point C.
Sliding the string hand ’C’ down toward the bottom tip ‘A’ shortens the distance A-C and lengthens B-C. These work basically as levers, and longer levers complete more work with the same force. Now, we're still drawing ‘C’ to anchor regardless, so since A-C is now a shorter lever, it is overpowered by side 'B' and tips that way. Hence, limb ‘A’ needs to be stronger to resist it and again establish balance.
In order for my example to act right, balanced at full draw, the left limb needs to be stronger. Stronger because of the force added to the bottom limb, not the top.
So, three under strains the bottom limb more than split, calling for a stronger bottom limb, and split finger strains the top more calling for a stronger top limb. Now, by stronger, I mean 'in relation to' being tillered the other way, not necessarily stronger as viewed at brace when compared to the other limb... but some truths are apparent there as well.
Art, you said, “When you hear someone recommend a 1/4" positive tiller for split fingers and an even tiller for three under, what you're really getting is a one-size fits-all approach to cover the vast majority.”
I'd say what you're getting is poor advice... since the opposite results in better-tillered bows in each regard.
Better advice is; To tiller the bow so that the limbs see equal strain at full draw with the fulcrum point under the bow hand exactly where the shooter prefers it in the grip, and the fulcrum point on the string facilitating his grip there(three under, split, etc)… while disregarding advised arbitrary ‘tiller measurements’, such as 1/8 or 1/4 positive, etc.
A bow tillered evenly, with its center at the center of the handle, and pulled by the center of the string, will show both limbs flexing equally. Yep, hard to dispute that.
If the same bow, tillered evenly, is pulled from above string center, the top limb comes around sooner, bringing the arrow nock with it, and must be strengthened so that it won’t. The converse is true as well.
It’s definitely opposite of the advice often given.