Very interesting thread!
To respond to Pete, it would seem to me that flycasting is a strict dominant arm thing for the vast majority. I think we all tinker with casting on both sides of our head for wind or just to say we can
I feel (nearly) symmetrically comfortable about Spey casting from either side when using a pulley to set up. I'll let Brian or Bob S. comment on how well I Spey cast lefty, but I 'feel' comfortable. In any case I reel lefty when Spey casting but have noticed that when I have the long rod tucked under the arm and a violent strike occurs, the reel handle bangs into my vest and jacket rat-tat-tat like a jackhammer when a hot steelie screams down river. The handle turned to the outside (righty) would not do that.
Reeling can go either way for me, but I do feel a lot better with the rod in my right hand when fighting steelhead or something that zigs, zags, races and leaps a lot. I'm not about to question Lefty's experiences, and Bob is also adamant about RH for tarpon, and he's done a lot more of that than I.
When I am in an obvious blitz, I throw and fish lefty. As a matter of fact I remember the first schoolie I caught while fishing entirely lefty, near the mouth of the Herring River on the Cape. I also remember the first steelhead I caught Spey casting lefty, above the launch at Blue Creek on the Cowlitz River in Washington State.
Through the years, I've reeled levelwind for salmon righty, level wind for steelhead righty and lefty, spinning lefty, push button lefty - all depending on availability more than preference. Since I don't really use that stuff anymore, I guess I always reel lefty until convinced otherwise.