This might be a little late, but what about greenscreen?

You can shoot footage of the doll house empty, then shoot the characters separately  against a green screen. If you are using a stationary camera, it would be easy to composite the two and it would be non-obstructive to the doll house. It will also allow you more room to manipulate your puppets.

Johnny_Brento wrote:

I guess that would make jumping manuevers a lot easier to accomplish than using Magnets or tie-downs.

For jumping and flying there was always the need for some sort of rigging for that purpose, however having said that, I don't think any system is better, or more sturdy than bolt tie downs, once the foot is there, that's it. With body rigs, there is always the chance that you will increase your workload by constantly putting the feet back where they belong, cause they slid during animation.  There is a reason it was adopted by the monster movies, because it keeps the puppets steady, in the days before frame-grabbers that was kind of important.