I use the three cards under the cut piles as well, in a method suggested by Rachel Pollack in Forest of Souls. She calls these three cards the "teacher cards", and reads them as being the main teaching that we will acquire from the reading - that is, the main teaching we need now. I have found it remarkably useful and accurate. I think it's close to the method you describe.
Oh - just one more thing. I put the three teacher cards back in the pack after I've looked at them, and then fan the pack out. The three cards frequently re-appear in the reading.
Thirteen - I also use the non-dominant hand method, including from drawing the cards out of the fan - and tell my querents to do the same when they are selecting cards.