The Ritva says that we may learn from this Pshat that Rabeinu Meshulem was of the opinion that even a minimal height is enough for a Kinyan Hagbahah. I presume that he was bothered by the fact that elephants do not jump, but nevertheless was satisfied that they are able to raise themselves off the ground in some minimal way.
Elephants cannot at all have 4 legs off the ground at the same time, even slightly (only the front two legs; the back two cannot lift above the ground together at all). Jumping even slightly is not possible anatomically speaking - "at no point do all their feet leave the ground" (See page 5 here: http://zootorah.com/essays/jumpingelephant.pdf) .
Your answer is therefore problematic. It must be that the Ritva received mistaken information from the relevant secular authorities. Also, I highly doubt that Ritva had this on his mind at all.
However none of this means that Rav Meshulam had the wrong peshat - he may well have been correct that this is what the Gemara meant.
(a) Here is what the Kollel replied to this question when it was presented to us in the past:
>>The Gemara is merely saying that if an elephant would jump, a Kinyan would be effected. It is not discussing a Mitzvah to do so, but rather that this would create a Kinyan. I'm sure the Gemara wasn't discussing a pressing every day question (as most people would probably not be Koneh an elephant in this way, even if it could be done). Whether or not elephants jumped back then, and our possibly saying "Nishtaneh Ha'Teva" if they did, is irrelevant to the explanation of the Gemara. All the best, Yaakov Montrose<<
If I am not mistaken, this is more or less equivalent to the conclusion that you reached in your fascinating article referenced above (p. 9). As you pointed out, Rabeinu Meshulam's suggestion would be just as Halachically relevant for a large dog, bear, lion or other heavy animal that can lift itself off the ground.
(b) About jumping "just a bit" - I don't know why you are so certain that the Ritva was not bothered by the anatomical question. Whether or not he or Rabeinu Meshulam ever saw an elephant (which you discuss on p. 8 of your article), the simple calculation (referred to on p. 4 of your article) that "the bigger they are the harder they fall" would cause anybody who heard a description of elephants to be skeptical as to their gymnastic abilities.
In fact, the Ritva conspicuously leaves out the word "Kofetz" (jump), mentioned by the other Rishonim when quoting Rabeinu Meshulam, and instead writes that the elephant "lifts itself" (Magbi'ah Atzmah) to eat the vines or twigs.
By the way, the word "jump" need not be taken literally. Rabeinu Meshulam may maintain that it is sufficient to cause the four legs of an animal to be removed from the ground in any manner. Thus, if an elephant is standing next to the edge of a mound and a person tempts it with a tasty branch to step off of the mound, if its four legs are off the ground even for a second before it hits the ground below it may be a valid Hagbahah. I do not know if this is anatomically possible or probable, but it is a more likely scenario than jumping elephants. (This type of Hagbahah is discussed by Tosfos Bava Metzia 9a DH Ho'il, who maintains that it is not sufficient.)
(c) You mention in your article a number of times (pp. 2, 7, 10) - and summarily dismiss - an enticing proposition. Perhaps Rabeinu Meshulam is referring to not to a jumping elephant, but to an elephant standing up on its hind legs in order to reach for a branch. This is quite plausible anatomically, as shown in a beautiful picture accompanying your article.
You reject this for a number of reasons: "Tosafos is definitely referring to the elephant jumping clear from the ground with all four feet, not rearing up on its back legs. His point is not in innovating a form of movement that is acceptable as hagbahah... The hagbahah itself must be a regular hagbahah, which, as always, requires that the item be entirely raised from the ground. Ritva likewise notes that the elephant must have all four feet off the ground at the same time."
Regarding the words of the Ritva, a close examination of the portion in question shows that he is using that argument to reject Rashi, who suggests (according to the Ritva's understanding) that Hagbahah can be accomplished "one leg at a time" when an animal places its legs one after the other on top of piles of twigs. Whatever Hagahah is - whether it means jumping or rearing up - it must be done all at once. The Ritva is not discussing how many legs must be lifted to be considered Hagbahah.
Regarding whether Tosfos' point is innovating a new form of movement that is acceptable as hagbahah - we must not lose sight of the full picture. Rabeinu Meshulam is trying to understand a Gemara. As the Ritva and Rishonim point out, he found Rashi's explanation unsatisfactory for a number of reasons. You succinctly described two of the problems in your article: 1. "If the Talmud were talking about building a platform, it would surely make more sense to speak of using stones or wood." 2. "Others raise the objection that a platform of vines would not be of legally different status than the ground itself." (3. Another problem with Rashi's explanation is the following. If leading an animal up a raised platform constitutes Hagbahah, why does the Gemara earlier (25b) tell us that if one places vessels under the four legs of an animal he can only be Koneh through Chatzer and not Hagbahah. Rashi here, sensing this question, found it necessary to posit that Hagbahah requires lifting an object three Tefachim - and vessels are not usually that tall.)
Rabeinu Meshulam proposed an answer to all of the above questions with his single suggestion. The brunt of his answer is that the twigs are used as elephant fodder (as in Shabbos 128a and elsewhere) in order to bring about Hagbahah. The explanation is elegant. But, as you ask, if elephants do not jump, where is the Hagbahah? (Your suggestion (p. 9) that "True, the specific example given of an elephant would not work, but Tosafos' explanation of the Talmud's answer is still relevant for other animals" - is not completely satisfying. The Gemara normally is consistent with its terms and does not use mixed metaphors.)
Thus, if the elegance of Rabeinu Meshulam's explanation bespeaks its accuracy, and if elephants do not jump, we can indeed suggest that according to Rabeinu Meshulam the Gemara implies that causing an elephant to rise on its hind legs constitutes Hagbahah. (As I mentioned, when the Ritva quotes Rabeinu Meshulam he leaves out the word "jump" and writes that the elephant "lifts itself.") So your scientific observation can be presented in a new perspective - Can we prove fromthis Gemara that having an elephant lifts itself on its hind legs constitutes Hagbahah?
Is there Halachic basis for such a suggestion? The Gemara in Bava Metzia 8a, 9a, tells us that if one lifts one edge of a Talis and the other edge is on the floor, it does not constitute Hagbahah. However, the Nesivos Ha'Mishpat (CM 195:2) posits that according to the Rambam it *is* considered Hagbahah for the part of the Talis that has been lifted, as long as nobody is holding onto the other half. But that would not seem to be enough to acquire the entire elephant, since there is no Hagbahah at all for the two hind legs.
One might suggest, though, a difference between an object such as a Talis and a live animal. A dead object is not inherently a single unit; it can be cut up into pieces each of which retains its original nature after being cut. However, a live animal is inherently a single unit, which cannot be divided up and put together. Perhaps a Hagbahah of most of an animal constitutes Hagbahah on the entire animal.
Alternatively, we may suggest that when Hagbahah is accomplished by causing the animal to lift itself, rather than lifting it like an inanimate object, it is not necessary for the animal to remove itself from the ground in its entirety. Since the point of Hagbahah it to demonstrate ownership, when one causes the animal to follow one's orders it is a greater demonstration of ownership than picking it up, and therefore less of a Hagbahah is necessary.