Keep Circulating the Tapes: You'd be hard-pressed to get a copy of the complete original network broadcast version on an actual tape, because the official home video releases had to cut out several scenes due to music-rights issues. And don't bother hoping Disney will release a Special Uncut Edition, since the video rights for Sesame Street, Fraggle Rock, and even Muppet Babies (yes, the main characters themselves in baby form) are owned by other companies. As of this writing, the uncut broadcast (with a few seconds missing at the beginning) is on YouTube.
The European release supposedly has most (or all?) of the songs intact, and is only missing a couple scenes. Still, don't expect it in America anytime soon. This cut was also shown on Canadian family network YTV until around 2003, and on Nickelodeon until the early 90's.
The full, uncut version of the special is available for viewing in the library at the Paley Center for Media in New York City and (presumably) at their West Coast branch in Beverly Hills, CA. The special is also shown for the public in the Center's theater during the Holiday season.