Go with what your comfortable with.
What you should see in those videos is another common among those shooters.
Any how I'm a LH shooter so here's a few in sights on my issues.
Military Prone. (Is how I learned growing up but also "forced" to shoot righty )
1. I feel as if all the weight is on my right elbow and I also tend to fade(lean) to the right. Throwing my natural point of aim off right and low.
2. I just can't get my left elbow up under me for solid support.
3. Between my flexibility or lack of and arthritis my hips don't like it. Also my back and neck arch adding some discomfort
If you know military prone and are comfortable with it use it especially at a "match" try new things at the range for practice.
Olympic prone= drawing your trigger side knee up along your side.
1. Shifts my weight just enough to feel balanced on both elbows.
2. I can get both elbows more "under" the rifle for support
3. My back is not as arched
Oh and many don't shoot well balancing on the belly