If you want to go the lefty route, and you want to play electric or amplified acoustic, you will have to get a lefty guitar. Simply restringing backwards may work on a plain acoustic, but the preamp controls for an acoustic/electric would be pressed against your lap if you were to play it lefty. If you have a cut-out to allow for upper fret access, it would be on the wrong side. Electric guitars are not symmetrical and cannot be restrung backwards to accomodate lefty players... unless you're Jimi Hendrix
His controls were backwards (and the pickup balance would be off, as some electric guitar pickups are arranged to have a bass and a treble side), which isn't practical, but he made do with what he had available, and obviously suceeded..
Left handed guitars, while rare and sometimes more expensive than their righty counterparts, do exist, and people do play them. Go play a lefty guitar at a music store and see if it's any less awkward to strum. Though I've heard contrary from lefty guitarists, Mama Bear does make some exellent points, and they wouldn't make lefty guitars at all if there weren't at least some demand for them.