I like your wild imagination - these are the kind of ideas that people say can't be done ... until somebody like Tom or Oskar makes them just a couple of years later.
They should probably join
these.
PS. I think your second idea should be possible - to create an interlocking burr puzzle, where each piece is a shape-shifting twisty puzzle, and must be solved into the right shape before it can be interlocked with the other pieces.
