Number 2 will do (?)

In an attempt to improve my methods another of Andrew's ideas came to mind: expanding foam. Usually you use this to fill gaps in walls. Whatever it touches while it's still wet becomes a sticky mess, but it's great at keeping stuff in shape. So I mixed up some papier mache from the remaining pulp and did this:

Frankly, I had a  hard time not drawing a face on this. The cup is smaller, far from a half-sphere, but should still be suitable to create an aircushion.

After allowing it to dry for about 5 hours (with an electric fan) I topped it off with expanding foam:

Yes, it doesn't look great, but it does the job. I left it overnight to dry and took it off the next day with this result:

It was still wet on the inside, but once it's dry it will get air-inlet holes centered around the south-pole and from hopefully will make the ball hover.