I would add that working on "both sides" with broadaxes or the adze or reversing hands while chiselling or, especially, shooting your round of arrows from both sides, not only eases the muscles but improves the technique(and, as Will writes, gives an advantage over the grain of the timber).
Using the opposing grip most often feels awkward, but I suggest trying it (maybe not on that 1000 dollar timber, though), see if you don't feel stronger coming back to your natural side.....

As far as left-handed goosewings go, I have finally discovered ebay, but still have not seen a left-handed goosewing, though i bought a right-handed one the other day almost as a joke, the price seemed very low, perhaps the steel will be bad?