One and a half unpublished pages of the message-in-a-bottle story exist, they went to fans out of Barks' "scrap pile". In reference to another story, Barks once wrote: "I often made such cuts in my stories whenever I detected any draggy spots. Usually this sort of cutting took place before the final inking." This story (and also the round money-bin story in OS 495) proves that this was not always the case.
There are two unfinished two-panel strips (quarter pages) that fit with published page 13. They are unfinished because they don't have the solid blacks inked in, but they are otherwise complete. This could mean that they were probably edited out fairly early, before the pages were finally finished and numbered. These two tiers are somewhat ambiguous in that it is not clear which comes first. One tier is a flashback in which a Beagle Boy recalls: "We slithered in behind this cliff and all the boys except me went ashore for the raid!" One of the Beagle Boys pictured says: "Quiet! This'll be a sneak job!" The next caption: "They climbed the cliff! I watched 'em! And then - And then -" The other tier has a scene on the boat. Huey says: "What?" and the Beagle Boy says: "Zowie! Just like that they turned to stone!" Huey says: "You expect us to believe that?" Beagle Boy: "It's the truth! Somebody did it! Maybe martians with a ray!"
Apparently these four panels were the second and third tiers of page 13, and the published third tier of that page could originally have been the bottom tier. This would make the published second tier new art which replaces the cut sequence. The information in these two panels is basically the same as in the cut sequence, only less extensive. Another reason why I have this theory is that published panel 4 is almost the same as the unpublished panel 3. Maybe the fourth tier of published page 13 was originally the first tier of published page 14? This would move the art one tier until the next spot where Barks changed the story, which might be on the very same page (14). Even though it remains theorizing and guessing, it could be that the fourth tier of published page 14 is new. Except for the dialogue, which could be rewritten, the first tier of page 15 follows the third tier (which would originally have been the fourth) of page 14 smoothly. Possibly the dialogue in published panel 6 of page 13 is rewritten, because the nephews could have warned for martians here instead of only saying: "Unca Donald! Unca Scrooge! Don't go up there!" The reason why I think that Barks added a new fourth tier to make a full page again is that he wanted to keep the rhythm in the story and didn't want to move up panels in page 15, which would make it a chaos and ruin the flow that is so characteristic for his stories. If this is true, Barks seems to have tried to stretch this sequence, because Scrooge's dialogue in the fourth tier is even a bit repetitive when compared with panel 2 of page 15 (although it emphasizes the important point that Scrooge is immune for the rays on the island).
One more comment on page 13: Barks could have rewritten the dialogue to smooth over the cut, of which published panel 2 and 5 seem to show traces. Judging from The Carl Barks Library - Set III, the Beagle Boy's words in panel 2 are incomplete ("So help me, ... turned to stone!"), which could mean that Barks forgot to complete it while revising it. The first one or two phrases in panel 5 look slightly slanted, which could mean that Barks added them later to replace what could have been said originally there.
Two other half pages are known. One numbered as the top of page 16 fits neatly immediately after published page 15. After Scrooge's cry to come up the cliff, Donald says: "I'll help you, Uncle Scrooge!" and one of the nephews says: "Come back here!" Donald tells the nephews they are worrying too much and convinces the two to come up with him and help Scrooge. In the fourth panel we see Huey, still down on the the beach questioning the Beagle Boy. There could be another half page between this and the published top of page 16. This bottom half of the page, presumably continuing Huey's interrogation of the Beagle Boy, is lost. Barks may have incorporated panels from it into page 18, where Huey asks: "Did you ever hear or see anything of whoever's up there?" When Barks retrieved it from his scrap pile, the half page was finished, except for the blacked-in areas. These he added before selling the art to a collector. The art even contains careful shadowing beneath the ropes on the bound Beagle, which does not appear in the published drawings.
The other known half page fits in place of the bottom half of page 17. The first panel follows smoothly after Scrooge's thought in published panel 4 that he must be too tough to be petrified, because he says: "Sure enough! I can hear the ray bouncing off me - Zing! Zing! Zing!" and then: "That means I'm safe while I get the boys out of danger!" The other two panels on this page are identical to panels 5 and 6 of published page 17, which are redrawn versions. Barks copied them almost exactly, changing only the beak on the petrified nephew: it is closed in the published version. The unpublished version can be seen as illustration here. The heavy black shading on the rocks on this half page came later, when Barks finished inking the half page for a collector.
Looking at these two scrapped half pages and the possibilities just mentioned, I get the following theory: Page 16 originally began with the unpublished half page which ends with the nephew questioning the Beagle Boy. This was followed by a half page of which the first two panels were cut and pasted as the second tier of published page 18. Possibly this half page ended with the first tier of published page 16, which would mean that no art is lost and that the bottom half of published page 16 originally was the top of page 17. (This leaves the second tier of page 16 as new art, meant to fill in the gap.) The published top half of page 17 originally was the bottom half. Page 18 started with the second unpublished half page in which Scrooge shows his immunity and which contains the alternate rescueing of the petrified nephew, followed by a bottom half which consisted of tier 4 of published page 17 and the first tier of published page 18. The bottom of published page 18 is new, made to fill in in a gap and to stretch the scene of Scrooge's investigation and capture (which contains more action than any of the two cut half pages). To show what I mean, I've made a reconstruction, rebuilding these pages as I think they could have been.
There's one big problem though: In the unpublished art the beak of the petrified nephew is opened, while it's closed in the published art. This could mean that the first tier of published page 16 (according to the reconstruction originally the fourth tier of that page) was revised, too. In the first panel a nephew says that he hopes unca Scrooge isn't mistaken, maybe he continued talking in the original version of the second panel? Also panel 7 of published page 17 has the nephews beak closed, which could mean that Barks did some more revisions and / or retouching to smooth over the cuts.
This could also even count for page 19 to 22, because these pages somehow also look like they were revised. Maybe Barks stretched the sequence in which the nephews are being threathened by the professor and his rays to give the story more action? (It could for example be that originally the nephews didn't plan to leave at all with the boat.) Whatever happened or didn't happen, without any art to prove it, this is driveling in the dark and there's already enough danger of that with having some of the left-over art. However, I'm quite sure that page 1 up to 12, and page 23 up to 28 are published as they were drawn, before any revision took place. They somehow seem to still contain the rhythm which seems to be lost in page 13 up to 22.
If this theory is true (or at least Barks's thought of substitutions rather than cuts), then it would mean that much less than a total of four unpublished pages is lost. And that the story wasn't intended to be a 32-pager at all.
Whatever happened, and as Kim Weston concludes, this story seems to have had a rough gestation period and required a lot of revising.
The scrapped art is published in The Carl Barks Library - Set III. In the two loose tiers, the nephews' sweaters, caps and the Beagle Boy's mask are blacked in. In Holland, the unpublished art was put back into the story (except for the overlapping scene of the rescue of the petrified nephew) for an album reprint, making it a 29 1/4 pager!