It seems you're really focusing on the force put on the bar and hardware from the dogbone. What is equally important is the force from the hammock, since you'll never have any load on the bar/hardware unless you're IN the hammock. This force can essentially be considered another "rope", as the tension is primarily held by the seams down the edge which stretch less than the fabric. Further, it will basically be another triangle, thanks to the majority of the weight being in the middle of the hammock, and the cat cut exacerbating the effect. The angle and "prying" force you have denoted in your drawing will essentially be replicated on the opposite side (although the angle and forces will be slightly different, but not substantially). Because of this, you won't have a huge moment (yup, right word!) about the edge of the pole nearest the dogbone, as it will be more or less negated by the opposite and not-quite-but-nearly equal moment on the hammock side. This is what forces the hardware "flat" against the end of the pole, and keeps the hardware from prying against the pole tip.
The problem with your bottle opener analogy is that the only force resisting the torque from the bottle opener (bridge hardware) is the bottle cap (pole tip), where in reality there's another force which will be nearly equal to that applied by the opener, and in essentially the opposite direction. It's more like trying to open a bottle with your left hand, but the harder you pry up with your left hand, you also press down on your left hand with your right. The forces on the hardware (and thus the pole tip) will always have a linear relationship, as it's due almost entirely (with a small change from your dogbone length) to your own body weight. More weight in the hammock will increase BOTH forces, and BOTH moments.
I see your paper drawing and raise you an even *more* ghetto MS Paint drawing, where the red in the left "image" is the spreader bar, with the dogbones to the right, and the hammock (with its exaggerated triangle shape) to the left.
Now, if you make the hole for the pole tip larger like you're suggesting, the small difference in forces will be more easily realized, as the hardware will tilt toward the dogbone (slightly higher force thanks to the angle you mentioned), creating a slight effect as you have illustrated. This will have the added effect of placing the force against the pole tip by the hardware further away from the face of the pole end, which will make the effect worse still. If the pole is a very tight fit, the hardware has no ability to rotate, and since the torque we're interested in is against the pole tip, and about the edge of the pole, you will have next to no force on the pole tip itself.
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