I'm not a big fan of arguing on the internet, but unless I have misunderstood you, I'm gonna have to disagree.
The only time a tripod will become unstable is if the force vector (the resultant angle between the line from the anchor and the line to the hammock) points outside the footprint of the tripod. The only way that can happen is if your anchor (backstay) is very close to (or actually inside) the footprint of the tripod.
This video might make things a bit clearer,
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Gadget
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