I posted a long diatribe earlier, but did some rethinking and have revised it. Here it is in its entirety.
BJ. I didn't envision the grip pressure causing the dynamic change in limb pressure, but it makes sense.
One other factor that hasn't yet been noted in this discussion is the height of the shelf above the center of the bow, which, in effect, determines the relative length of the top and bottom limbs. Most bowyers place the shelf about 1 1/4-inch above the center of the bow, but some place it as much as 2 inches above the center of the bow. (For some reason, I've been recording these measurements on bows that have passed through my hands for about 30 years.) In the first instance the top limb is longer, in the second instance, the limbs are about equal length.
I point this out only to demonstrate that where the arrow shelf is cut determines where we place our fingers (and bow hand grip) in relation to the center of the bow, which in turn impacts the vertical torque on the limbs and how we adjust to it by adjusting the tiller (on an ILF) or the nock point.
I should note, too, that my records show that most bowyers who cut the arrow shelf 2 inches above the center of the bow, which makes for equal length limbs, tend to make the bows equal our neutral tiller, whereas most who cut the shelf 1 1/4-inch above center, in which the top limb is longer than the lower limb, give their bows a positive tiller.
Having said all of this, I'm still having trouble clearly explaining the string length vs limb flex question. Let's try again. First, if you short string a bow, it will flex the limbs more than the bow braced to its standard brace height. A shorter string will flex the limb more than a longer string. There's no reason this principle shouldn't hold on a half a bow as well.
Since most bowyers place the arrow shelf 1 1/4-inch or so above the center of the bow, the top limb will be longer and the shooters fingers will be above the center of the bow, whether shooting split or 3-under. If the nock point is then moved up further, the string length to the end of the bow becomes shorter, flexing the limb more. The 1/4-inch positive tiller built into the bow weakens the limb just a bit to accommodate the greater flexing to balance it to the lower limb.
By comparison, the bottom limb (and string) is shorter to begin with than the top limb and thus is built a bit stiffer because it will flex less on a bow with with a standard 1/4-inch positive tiller. In this case, moving the nock point and fingers up creates a longer string below the fingers, which one would reason would flex the lower limb even less, requiring even more stiffness. Yet, we know that a neutral or zero tiller works better for 3-under shooting. However, I postulate that the string lengthening that occurs between the lower fingers and lower limb tip in effect also lengthens the lower limb vis-a-vis the upper limb, balancing them out and coming closer to neutral tiller. I.e., because the limb becomes longer, it is flexed less than if it were shorter, which in turn requires a little less stiffness, i.e. neutral tiller.
Keep in mind that all the differences we're talking about here are very small, a half-inch or less. My discussion above tries to indicate the relationships between the variables, but the variables are so small that most folks won't notice them. That's why switching from split to 3-under or vice versa only requires a small change in nock point height.
Anyway, that's my story and I'm sticking to it. Plus, my head hurts.