Player in field of play leans across the plane to touch the ball. Arm in touch therefore ball in touch.
Under my suggested wording - which is precise - The arm is in touch - the arm is touching the ball = the ball is in touch
Player with ball in left arm swings right arm through the plane of touch. Does the player's arm no longer count as being in touch?
OK that bit needs work... I think it would be a hard call to say that this was touch.
Perhaps:
The ball is in touch when it touches or is touched by anything which is itself in touch.
For the purposes of this Law the referee is regarded as a player; for clarity, Touch Judges, Assistant Referees and other officials are not.
Objects, animals and non-players are in touch if they or any part of them is beyond the plane of touch.
A player is in touch if any part of that person has touched the ground beyond the plane of touch, and the player has not yet, while on his feet, placed both feet on the ground inside the plane of touch before he next touches or is touched by the ball.
A Player who jumps from the field of play to play the ball must land with both feet inside the playing area, or the ball is deemed to be in touch when he played it.
If the ball is touched by or touches a non-player in the playing area the referee stops play and judges what would have happened next had no such contact occurred, and restarts accordingly. In cases of doubt or where play would have continued without a score or touchdown or the ball otherwise going dead, the referee may award a scrum where the contact took place, or at least 5m infield from any goal-line or touchline, with the put-in to the side he feels appropriate.
Which does actually allow the reach over, but I can live with that. It doesn't matter if a player jumps from in touch and catches the ball outside the plane - he can catch it inside the plane. He cant jump from infield to play it unless he lands infield.
But no doubt there is some weakness....