One of the real advantages of a double is without doubt the possibility to load a solid in one barrel and a soft in the other. I think the makers of good doubles are aware of this fact and they design their locks accordingly. So it should be no problem to fire either barrel first without the risk of doubling. Also I believe that that the POI will not change too much at reasonable hunting distances if You discharge the left barrel first, at least if You use open sights.
So I wonder where the problem is !

Kalunga

"In my profession my needs are few, a dependable rifle, a cool nerve and a really good pair of boots !"