Learn English – the meaning of “tap dance to work”

Fred Astaire and Ginger Rogers were famous dancers in, umm, the 1940s I think.

Fred Astaire was a very skillful dancer, performing many complex and difficult moves on the dance floor.

But humorist Bob Thaves once noted, "Sure he was great, but don't forget Ginger Rogers did everything he did, backwards ... and in high heels!" That is, when Ginger Rogers danced with Fred Astaire, she had to make all the same complex and difficult moves he did, but on top of that, as the woman she was dancing backwards while he was moving forwards, plus she was wearing high heels while he was wearing flat shoes, which surely made it more difficult still. So the point is, he was saying that Ginger Rogers's job was even more difficult than Fred Astaire's. (As I don't know anything about dancing, I have no idea if this is true. But that was the point of the quote.)

I don't think the original author was trying to say that Mr Roberts went backwards, but rather simply that the task he was trying to accomplish was very difficult -- like dancing backwards.

So without the allusions, the writer was trying to say something like, "This was a very difficult and tricky task. It's one thing to do X in general; it's even harder to do X under these circumstances."

I doubt the average young American would recognize this allusion. I'm 53 years old and I think it's fortuitous that I happened to recognize it. I suspect most Americans under 40 have no idea who Fred Astaire was, never mind recognizing the quote.

Houdini is better remembered, so yeah, I think most Americans would at least know that he was a renowned escape artist.

On the flip side, I'm only vaguely aware that Jersey Shore is some TV show popular today. I know nothing about it. But maybe it's well known to young Americans.

Now that you mention it, that was quite a set of cultural allusions to include in one brief quote. I wonder if that was deliberate or if it was basically a coincidence.

There are two distinct uses of "killing it" in your question. The first would be used as such:

You killed it out there! The crowd loved it!

This meaning is more or less explained by the question you linked to:

While its usage to mean "very funny" is partly covered in another question, its usage via idioms like to make a killing to indicate a "large profit" dates back to 1886 (as noted above).

This most likely extended to include individual performances, financial or otherwise.

The second usage is the connotation you describe in this paragraph:

Peculiarly, "killing it" also seems to hold the connotation that it has been done so well, that it is no longer fashionable for anyone else to do a similar performance, because it has 'been killed'. And though I could not find a citation for this, this appears to be implied where I have heard it used in speech.

This is related to the concept of a thing being "dead" and isn't related to the first usage. From the dictionary:

dead: no longer current or prevalent, as in effect, significance, or practice; obsolete: a dead law; a dead controversy

To kill something is to make it dead; in the context of plays and songs they die by phasing out of cultural relevance.

A good example of these are genre killers:

Genre Killer — One order of magnitude greater than Franchise Killer, this is when a work somehow manages to take an entire genre down. A rare and unpredictable phenomenon that can, in extreme cases, cause a genre to become Deader Than Disco.

Of note, these are not necessarily successes. You can kill a genre with a terrible performance. From the TVTropes link, here are two notable examples from Hollywood:

Cutthroat Island was an attempt to revive the swashbuckling adventure movie. Instead it just sunk it farther down into its grave, along with Carolco Studios, the careers of almost everyone involved, and (along with their other collaboration The Long Kiss Goodnight) the marriage of star Geena Davis and director Renny Harlin. The genre was not exactly a thriving one at release, but this made sure no one would even attempt another shot at it. Even after the success of Pirates of the Caribbean, no one seems interested in pirate movies that don't belong to that franchise.

The Jurassic Park films are an example of one series' smash success making it impossible for subsequent films to live up to it. No one has bothered to make a serious dinosaur movie since, and all films and video games that have happened to feature dinosaurs, have, without exception, contain conscious nods to the franchise.