I have used the DMM large swivel like this quite a lot, both with 2 climbing systems, a lanyard, and the hook.
Remember that the lower ring in not held statically. In my experience, the upper ring will tend to orient itself along the axis of the swivel.
The lower ring is in equilibrium, and the only force that really matters is that acting on the swivel(1A). As long as the lower ring is able to rotate, the upper will necessarily orient itself well along the axis of the swivel.
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