David,

If you want a heli which behaves more like your original description, i.e. has positive stability, get a coaxial rotor heli like a Blade CX(2). These are very fun for flying inside your house or office, and will hover hands off once trimmed correctly. These are mainly for indoors since they can't tolerate much wind. They can't do a lot of the things that a conventional heli can do, but unless you're a really expert flier you'll actually be able to do more with a coaxial heli in a space as small as a living room. It's only when you go outside or into some gym-size indoor area that a coaxial heli starts to feel limiting.

As far as the neutrally stable vs unstable question: I'd say that in principle helicopters are neutrally stable, but in practice, micro helis behave as if they were unstable. Maybe in a perfectly calm environment, where somehow even the air coming from the rotors wasn't creating any turbulence around the heli, it would exhibit neutral stability. In practice though a micro heli is constantly being upset by air currents, not to mention the fact that most micro helis aren't made from extremely precision parts. So to go back to the "balancing a marble on a sheet of glass" analogy, for micro helis it's as if your kid brother were standing nearby randomly tapping on the sheet of glass from time to time while you're trying to keep the marble still.