I was a right handed southpaw for ages......from a family of right handed southpaws going back to the time of Jack Dempsey!
I do try and train both stances equally now though because my straight right from the orthodox stance is stronger than any of my right lead punches from the southpaw stance!!
As for the straight left, a half decent opponent will figure out fairly quickly that it isn't your strongest punch and exploit that by circling to your left and looking for openings for their right hand (hook or straight). This in turn would mean that your right hook would have further to travel for contact.
I also noticed that it was easy for my left to drop below chin level. I'd honestly consider adjusting to orthodox or seriously improving your left hand.
Strangely I found myself using my left hand more as a left hook than as a straight, the punch seemed far stronger than my straight left. Check out Calzaghe vs Eubank round one (the knockdown punch) to see how to throw this punch well from the southpaw stance.