The Spain Mutiny (Cartoon from failed Three Stooges pilot)

It was reported to have been screened at a past Stooges convention, courtesy of a collector, and I'm pretty sure the Stoogeum has a print on file.

As for getting a copy for yourself? Nah, the individuals who have prints are terrified of having copies escape for fear of "devaluing" their hoard.

The Stooges' last picture, Kook's Tour, has turned up recently on a pristine, non-faded 16mm reel presumably from Norman Maurer's collection, but the seller wanted upwards of $35,000 for it. I hasn't turned up on Ebay again recently, so I don't know if the seller gave up or if someone paid the ransom?

I think it was mentioned at the threestooges.net message boards, now referred to as The Kingdon of Moronika. I used to frequent the discussions until the board deteriorated under the auspices of one moderator who, sorta indirectly, turned it into a blog of his own musings about music, sports and film reviews, where threads rambled off-topic and NSFW images were allowed.

If the Stoogeum has a copy, I'm pretty sure you could arrange a visit and a screening. Not sure about Covid restrictions but, in the past, visits were by appointment only, and you pretty much get the run of the place for a few hours.

On the subject of rare film, the updated Three Stooges Scrapbook mentions an animated test film from, I think, Norman Maurer productions, where Moe Howard voices a pirate. This film was created, allegedly, using a rotoscoping animation process not unlike what was proposed as a plot device in The Three Stooges in Orbit. I need to glance through that book again for the details, but it is a very rare bit of film.
<Edit>
Just looked it up, and it was called the Artiscope process. The Film was titled "Captain Lafitte" and it pre-dated The New 3 Stooges by nearly a decade:



Also, just something to think about: The Three Stooges Scrapbook includes a photograph of a chunk of several frames of the very lost and unused reel from "Plane Nuts" with Ted Healy (the one where they were supposed to fly around the world backwards!).



Wonder where that clip of film came from, who had it, who trimmed it, and why the rest wasn't kept? Nitrate decomp? Trashed?

I think you got the details wrong a bit
The live action bits in question for theatres was remade from the ground up with nods to the pilot for the film "The Three Stooges in Orbit"
The cartoon did pop up in the film but for a minute in one scene
While the film is nearly beat by beat of the live-action bits from the pilot, they made new scenes to pad it out 
however, The Magic MacGuffin that saved their show (at least in the film) was "Electronic Cartoons", which is primarily a derivative of "Colormation", a short-lived process made by Leon H. Maurer (one of Moe's relatives)

this is proof that it's the same technique as the "electronic cartoons" in the film

Man so I nearly missed the mark with my knowledge in that case. I had only seen bits and pieces of In Orbit and assumed that any scenes from the Stooges Scrapbook used in it were very minimal rather than being a large portion of the film’s plot. So in actuality the lost media here is the full cartoon and original theatrical version of Stooges Scrapbook as a whole.