Ryjak, it's funny you bring this up, it's a topic I've thought quite a bit about for both Firestorm Armada and Halo: Fleet Battles.
Ruckdog's idea below could work, I think. One thing that I always keep coming back to is how to determine when ships are in the cloud. For Firestorm, the flight peg has to be in; for Halo, the middle of the base is what counts (essentially the same thing, except the bases are bigger). With Ruckdog's idea below, you could shift the cotton around to accommodate the ships once they are in the cloud.
The other idea I had was to build a sort of cloud "fence", roughly oval in shape, made up of several stands with armatures like Ruckdog mentions below. They wouldn't be actually connected, so you could "open" the fence for ships to move in. That method would at least make it look as if the ship was surrounded by cloud, but now that I think about it, it might make it difficult to measure to/from the ship.
Ruckdog, did the cotton get brittle after the paint dried?