Rebel,
It does not seem to me that the Apache style should hurt your shoulder. It will, of course, if you do it wrong. I know this by having done it wrong for awhile.
Reading Forsyth's account again, I have been impressed by how he described the old Apache grandfather: calm, unhurried. I think that he would not have so appeared, were he trying to force his slinging. Thinking about this, and observing my own best throws, I have come to the conclusion that my arm -- and your arm -- should be an extension of the sling. Lift your arm from where it rests at your side, but from there on most of the power should come from twisting your body around, and your arm and sling will just transmit that power to the stone.
When I have managed to do this, my throws have been more powerful and have felt less effortful.
After your shoulder has healed, try the Apache style again. Do not try for power at all, at first, just work on form. The power will come when the form is right.
As for underhand, it is not one of my favorites right now. I sling tennis balls for my dog, and I have trained myself to release late, lest I strike the dog in the face -- he is usually dancing a few feet in front of me, waiting for me to sling the ball, and so standing right in the line of fire, so to speak. Unfortunately, I keep on releasing late even if the dog is not there, and so my accuracy suffers. On the other hand, if I lob something underhand, I drop on target quite often. Underhand would thus be a good technique for, say, hitting ground squirrels in the garden without damaging my wife's vegetables...
I note also that in the "O-SAST" discussion, TechStuf wrote that he cast a stone 278 yards with the figure-8 style, and
384 yards with the underhand style!