I am also right handed and left eye dominant. In fact, I cant even close my left eye by itself. I started shooting more seriously in the last few years and someone recommended since, I was really just starting, that I should shoot left handed instead. It really didn't take long at all and now it feels foreign to grab a gun with my right hand. I also ended up being a much better shot left handed. Typically, it is seen as a disadvantage to be a left handed shooter, but since I have switched, I have noticed many advantages. Such as, having dominant hand to fight with, push, stab, lift, carry something such as a child, open doors, etc.. Also, if carrying on my left side I don't have to fight with the seatbelt buckle when driving.
There are many more small advantages that I wont bore you with. My point is it didn't take a lot of work to switch over to shooting and carrying lefty. Smith & Wesson M&P's are also completely convertible to lefty. Also, except for the slide release Glock is also now convertible as well. The slide release usually is not suggested to be used in a defensive situation anyways. Good Luck!