From a physics perspective, the only thing that matters is how far away from the center of rotation (the hull in the water) your righting mass (your body) is.
This is absolutely correct. The boat doesn't "care" whether the line is over the hull, under the hull, or if you use a pole, etc. The only thing that matters is the location of your center of mass relative to the axis of rotation. Different line positions may make it easier to hold onto the rope, but they have NO affect on whether the boat comes up or not. It's also important to consider wind and wave conditions as these will greatly help or hinder your righting success.
As for using your trap harness to right the boat, I like to throw two wraps of righting line around my hook and then just hand hold it. This provides enough friction to easily hold my body up with one hand, yet as soon as I release the line, it will easily slide out of the hook.
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