It has always come to mind that using 2 balloons would provide a slow and controlled descent of the payload. Parachutes won't open at high altitudes because the atmosphere is too thin. So usually, after the balloon pops, the payload starts plummeting and spinning like crazy until it reaches an altitude where the pressure allows the parachute to open. During its crazy nose-dive, the payload, the load line and the parachute itself are very likely become an entangled mess with the whole thing hitting the ground at free-fall speed. Plus I fear the antenna will break as well.
How to prevent this?
Well, Kyle has reported his experience using 3 balloons. The theory is that when 2 of them pop, the 3rd one doesn't have enough lift and starts going down smoothly. I'm really looking forward to him elaborating more on his blog.
Also check out Todd's write up. He used a parachute and a ring to prevent the parachute lines from tangling during descent.