A slightly different perspective that doesn't really answer the question at hand but may offer a different way of looking at it:
I'm in a strange position: I'm naturally right-handed, but when I was a baby, the nerve in my right arm was damaged. Ever since, my right hand has been slower and weaker than my left. I write with my right hand (fine motor skills) but open jars and throw balls with my left (gross motor skills); since I'm actually right-handed, and my left hand SHOULD be weaker than my right, this has given me the appearance of unusual clumsiness and lack of strength. With instruments, I've always played right-handed. The one real problem with this is that in most instruments I play, it's the right hand that needs to be the quickest and strongest one. On an instrument such as the flute on which both hands have to do approximately the same amount of work, I'm held back by both the fact that my right hand is a little slow and the fact that my left hand is not dominant. On the ukulele and other stringed instruments, as well as the piano and the accordion, I sometimes feel as if I am pushing my right hand through mollasses. The type of picking I do (with all four fingers at once) gives me the illusion of the sort of speed I am otherwise physically incapable of attaining. However, I am also hyper-aware that my left hand has its own job to do, and that requires speed and dexterity as well, a fact that becomes apparent when I play plectrum instruments such as the mandolin. The left hand's job, on stringed instruments, is often more fiddly than the right's. In other words, when I play stringed instruments, my natural inclinations are reversed; I use my right hand and arm for the job that involves strength and speed and my left for the job that involves manual dexterity.
Long story short: with almost any instrument, both hands have a job to do. I do think that part of the reason I don't have a problem reversing the natural inclination of my hands when I play stringed instruments is that I see music as moving from left to right: on the page, up the piano keyboard, up the fretboard. Left is low, and right is high (the exception here is in wind instruments, in which right is low, and left is high). Even though my left hand is stronger, I couldn't use it to strum or pick because I would see that as backwards and get confused. Genuinely left-handed people may see music as running from right to left (I couldn't say), but considering the orientation not only of almost every stringed and keyed instrument but of music on the page, they may not. Maybe it depends on one's musical background; a lefty trained in piano and/or written music may be more inclined to succumb to the right-handed view of the musical world.
(These are just random thoughts. Please forgive any ignorance in the above.)
