Not a big fan of SOB or nearly-SOB carry. I like a nice strong-side, IWB preferred, OWB after that, and then a quality shoulder rig(1) for lots of reasons over SOB. (Maybe if I had a choice mustache and drove a red Ferrari I might think otherwise.)
I think that we ought to keep in mind that "everyone ain't like me." Meaning, what works for me may not work for thee. In some cases this is due to injury, body shape, or other factors that are beyond the control of the CCW-er and not necessarily the sign of a newb or a fool.
The OP may be both, but I'll assume he is not and, after voicing my preferences for strong-side carry, I think it helpful to actually attempt the answer the query.
First off, one is no more compelled to sweep oneself with SOB than one is compelled to sweep one's hand/arm when carrying cross-draw or a shoulder holster. It just takes an understanding of where the muzzle is pointed and training to keep it from intersecting one's body by manipulating body or pistol.
It requires 5 seconds to demonstrate live, but 15 minutes to describe.
(Assuming "palm out" gun/holster orientation, where the butt is pointed roughly to the right on a right-handed shooter. Requires vertical lefty holster or left-handed cross-draw holster in SOB or near-SOB position.)
1. Get palm-out grip on pistol butt.
2. Draw IOW the angle of the holster. Up for vertical, Roughly 45deg for cross-draw.
3. Maintain wrist orientation: don't pronate, supinate, or rotate wrist through step #5.
4. While maintaining pistol, hand, wrist, forearm, and upper arm in roughly the same vertical plane, swing forearm (& wrist, hand, & pistol) away from body centerline (as viewed from behind), using your elbow as the main hinge/axis, until the muzzle is pointing directly at the ground and pistol is roughly vertical. This ought to bring the pistol out from behind your back.
5. Swing/rotate pistol forward, keeping muzzle from crossing your body. Once the pistol is at your body's centerline (as viewed from the side), it is similar to a strong-side draw, manipulation-wise.
It requires some practice and is slower than strong-side. Also, strong-side provides less opportunity to sweep your body. Others have pointed out retention issues. These are all good reasons many prefer strong-side over SOB.
(1) I have gotten to the place where I am no longer promiscuous with my CCW and have quality IWB, OWB/pancake, and shoulder holsters for my primary CCWs.