It's a quote from Speed. It's not so much a singular family joke, as a well known movie line at the time.
The note reads entirely as though it was written by a young man. The movie quotes, "foreign faction" etc all sound very much like an immature man's attempt at what they think a criminal group might sound like.
The crime itself also would be far more likely to be a young man. It's the kind of crime that would normally "ramp up" from acts like peeping, flashing etc. It's very unlikely to be the go-to for a family cover up, especially when it would have been far easier to explain a head injury on the spiral staircase or any other number of likely childhood mishaps.
Absolutely it would have taken time to write, and was written in the house. Given no handwriting expert could prove it was written by the family, the house had an open door policy at times and at least one door had been left unlocked its far more likely someone had entered the house and was waiting there whilst they were out.
The trace dna was found on her underwear, tights and under her nails. Too small a sample to be definitive, and yet in too many places to make sense as coming from anyone other than family (ruled out) or the perpetrator.
I think it was a family friend, neighbour or even colleague. Someone who knew the house, knew the family and potentially did plan a kidnapping. But like in the Lindbergh case, their plan went awry. It's just a shame it'll never be proven either way, and that little girl won't get justice.