every video or other account I have seen of these type of saws suggests either making it into a bow saw as you did or suspending it between two trees and sawing horizontally by moving the branch back and forth.

it does not seem like holding on to the rings and trying to use these things directly is an effective way of sawing at all.
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Warning - I am not an expert on anything having to do with this forum, but that won't stop me from saying what I think. smile

Bob