Lucky Dog.
I am left handed and right eye dominant. To shoot shotgun, I have to patch my glasses while shooting left. If I shoot Shotgun right handed, (when I forget my tape) I am just a little slower in my mechanics.. Shooting Rifle, I don't do anything (using a scope mitigates that need to patch as you lose peripheral vision) and shoot left handed.
Shooting Pistol is great, I am ambidextrous.
To answer your question, I can shoot, chamber another round and shoot my right handed rifles left handed faster than a right handed person can.
You take your right hand off the forestock and operate the bolt is all
I would not buy a LH action myself. I am too used to shooting left to change, and if there is no speed difference, why bother anyways?