What Neff said, get somebody to simulate the precession of the top while you figure out how to untwist the string and when to go under the top. You go under the top when the tip is pointing towards the hand that's doing the movement.
After you get the top in the trapeze and close the loop you will need to use your non-throwing hand to untwist it while waiting for the right moment to start the barrel rolls. You may want to get the movement down first using a bearing top, specially this untwisting.
By the way, what you meant was half-barrel rolls, not half-orbits. But you should do them with your throwing hand: the movement of the non-throwing hand does not regenerate much, if any.
