A balloon is only moving as fast as the wind. For all intents, it's relatively stationary within the wind current so only the relative speed of the drone is an issue. An out of control drone has issues at 150 feet. Under control, the operator...
The material used on balloons isn't nearly as fragile as you think. It also won't "pop" like a latex balloon. And, a balloon can actually stay aloft quite well with a drone sized hole, as long as the propane holds out, allowing for a controlled...
Call the FAA. Ask them.
And if they say you can do it, contact the people who own the balloons and let them know you'll be doing it.
They might be delighted to see your video.
Remember, if you're doing it purely for entertainment, you don't...