My wife and I are both lefties that play right-handed. I started on the 5 string banjo. I've never seen a lefty one of those. When she took up the bass I told her to just learn right-handed as she'd have a hell of a lot more options as far as instruments go. Plus I like having my dominant hand on the fretboard. After a lifetime of using right-handed scissors, power tools etc... it seems like really no big deal. If that is the sort of thing that hangs you up, you should probably take up piano. I have recently met 3-4 right handed folks that play left handed, though. One was a trumpet player that it made sense to just flip the guit over and play lefty. Another taught himself to play as a toddler on a toy guitar and when he took lessons they tried to make him play righty. But he'd already taught himself to play left handed. Visually I always like the image of the guitar/bass being opposed in their handedness. You know one guitar pointing one way, another pointing the other.
I'm not entirely sure you actually read my post. In most things, I'm right-handed. I know how to play guitar right-handed. I started playing right-handed. I switched because I broke my left arm as a child and can't turn that wrist enough to fret effectively, and this became worse as I was leaving my teens. I didn't want to switch to playing left-handed, but it was basically that or give up any hope of playing guitar for more than ten minutes at a time. I play left-handed because it's pretty much my only option, though I did have a great opportunity to learn how I wanted, since I already knew how to play I was able to teach my hands to play certain styles better, and to give up a lot of my huge reliance on pentatonic scales that I have playing right-handed.
As far as playing piano, well. I don't really care for the piano, it's to me about the most boring instrument to play. But I do play my synths a whole lot, and I have trouble with my left hand there too, since my wrist is so problematic. Nothing major, but I can't really cross my left hand over my right for anything. Also, if you don't know about a left-handed banjo, go make one!
Just for amusement, left-handed piano. And opposition.
The opposition is pretty meaningless. "Oh no, a lot of people do it like this, so should you!" Isn't that why they used to kill left-handed babies? Onto the intriguing thing, the left-handed piano is actually a very powerful idea. I've read some thing's about how most instruments are set up as they are because most people favor their right ear, and can follow melody better. This is why the lute, guitar, &c. are played as they are with the left hand doing the harder work. The really interesting thing about this backwards piano is how it will not only fit the pianist's hands but probably his head as well.
Also, on the Rondo Guitars, I've never played an Agile but I do have an SX I got for alternate tunings and I have to say, I didn't know you could get so much guitar for $150 unless someone's got a monkey on their back! I definitely recommend checking them out; they're very well-made instruments from all I've seen and heard.