I'm left-handed. I cast with the rod in my left hand, I switch the rod to my right hand and then reel with my left hand. Reeling takes more dexterity than holding a rod, IMO, and feels better in my dominant hand, but I also feel that casting with any type of precision also is better suited to my dominant hand, so I just switch hands after casting, sacrificing 1 entire second (the horror).
Seen enough pros do it on the tour and if it's good enough for them when they have money on the line, it's good enough for me. I have never missed a fish while switching hands.