One factor is I used to say that if the Beast out of the Sea does claim to be the Islamic Mahdi, that I doubted the second assumption of The False Prophet aka the Beast out of The Earth claiming to be the Islamic Isa/Jesus would be correct.
Then I changed my mind on that as I learned more. I showed from Scripture that the False Prophet being a Counterfeit Jesus does make sense independent of reading Islamic eschatology into it. But now, I've again noticed something others talking about Islamic Eschatology miss.
The Koran, which doesn't mention The Mahdi, does mention a Beast of The Earth, it actually calls it that, but doesn't depict this Beast as Evil, it's depicted as good.
And when the Word is fulfilled against them (the unjust), we shall produce from the earth a beast to (face) them: He will speak to them, for that mankind did not believe with assurance in Our Signs.And from a Hadith, though it's considered weak.
— Qur'an, sura 27 (An-Naml), ayat 82
Narrated Abu Hurairah: that the Messenger of Allah (ﷺ) said: "A beast will emerge from the earth. With it shall be the ring of Sulaiman (Solomon) and the staff of Musa (Moses). It will brighten the face of the believer, and stamp the nose of the disbeliever with the ring, such that when the people gather to eat, it will be said to this one: 'O believer! and to that one: 'O disbeliever!'"Could this Brightening the Faces have some connection to the Mark of The Beast in the Forehead?
— Jami' Al-Tirmidhi; English: Vol. 5, Book 44, Hadith 3187; Arabic: Book 47, Hadith 3490
Many Christian commentators think The False Prophet will claim to be the Prophet like Unto Moses. This beast claiming to have the Staff of Moses could fit that. The New Testament tells us that Prophet is Jesus. But many even claiming to be Christians want to give that title to someone else, like Muslims arguing it was Muhammad. And those who want to make Moses one of the Two Witnesses say this Prophecy is about a second coming of Moses. I haven't seen it yet but it wouldn't surprise me if some Jews think that will be fulfilled by Elijah.
Since The Mahdi was added to Islamic Eschatology later. One could argue that the demonic forces behind The Koran originally just intended Isa to be the Antichrist and this Beast the False Prophet.
But maybe it's possible for a Muslin today to try and argue this Beast in this Sura was a symbol of Isa, just as the New Testament Apocalypse Symbolized Jesus as the Arnion (usually translated Lamb but could be Goat or Ram). And indeed The Beast out of The Earth has Horns like an Arnion. And Jesus did Descend into the Heart of The Earth. Contrary to what most Muslims think The Koran doesn't contradict Jesus dying on The Cross but affirms it.
Having The Ring of Solomon could be a sign of being an Heir to Solomon and thus being Messiah Ben-David. But in this extra Biblical Lore about Solomon (it's not unique to Islam) Solomon used this Ring/Seal to perform Magick and control Demons/Shedim/Jinn. The Ring is also said to have the Divine Name in-graved on it. And I would guess it's normally depicted as being worn on the Right Hand.
This is perhaps a good time to remember that the number 666 was linked to Solomon, and the Hexagram has been linked to the Seal of Solomon, which many have sought to connect to the Number of The Beast. And in one Legend the Ring of Solomon is thrown into the Sea to be returned to Solomon later by a Sea Animal.
What if the Ring of Solomon here is going to be used like a Ring a King would give to a Regent?
More importantly, there is a reason the Ring of Solomon and Seal of Solomon are treated as synonyms when you study this lore. Because a King's Seal was often on his Ring which he would use to place his Seal on documents and so forth, but he might also give the Ring to someone else to give them authority to seal things in his name. Revelation is definitely drawing on this imagery in Chapter 7 with the 144,000. And The Mark is frequently viewed as Satan's inferior copy of that.
The Hebrew word chowtham is often translated either Signet or Seal. There is no Bible verse directly telling us Solomon had one. But the first one mentioned is Judah's in Genesis 38:18. Jeremiah 22:24 tells us it's often kept on the Right Hand. 1 Kings 21:18 tells us a royal one was used by the Northern Kingdom at least. The use of this word in Exodus 28:36 and 39:30 I've considered passages a False Messiah could use to justify the Mark of The Beast system as being part of The Torah, (along with the Tefflin verses). The Hebrew word translated "engravings" in those verses, pittuwach, is very likely the Hebrew equivalent of the word translated "Mark" in Revelation. Though another candidate would be miqla'ath which is possibly used as a synonym for that word the only times it appears, in 1 Kings 6.
Again, my take on studying these False Prophecies is that I think Satan makes all of them as potential seeds for The Antichrist. But that doesn't mean for certain that this false Prophecy is what The Antichrist will wind up using.