Is Jesse really Ishmael, as Muslims claim?

Ishmael and Haggar                            Jesse, father of king David

As I have explained in previous posts, Muslims believe that Mohammad is prophesied in the Bible because the Qur'an tells them so. This has led to all sorts of imaginative interpretations of various verses in an attempt to find that elusive prophesy.
Recently my Muslim friend directed me to a verse in Isiah (11 1-2): And there shall come forth a shoot out of the stock of Jesse, and a twig shall grow forth out of his roots. And the spirit of the LORD shall rest upon him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and of the fear of the LORD.
Jesse, he and they say, actually refers to Ishmael (the father of the Arabs and thus an ancestor of Muhammad). Many Muslim sites repeat this, including Islamawareness. How they arrive at this conclusion is interesting, to say the least.... 
 To understand this prophesy we need to study the verses carefully. These verses tell us that the rod (branch) which shall grow out of the stem (trunk) of "Jesse" shall be filled by God with wisdom, understanding, council, might, knowledge, and the fear of God. In other words, he shall be a statesman, a prophet and a judge. The obvious question that springs to mind is: Who was "Jesse"? In the Encyclopedia Biblica we read that Jesse is a contraction of Ishmael, or: "Jesse, for Ishmael… The changes which proper names undergo in the mouths of small children account for a large number of these particular abbreviations - who could guess, to take modern examples, that Bob and Dick arose out of Robert and Richard? … such forms as in ai were particularly common in later times … and many more in the Talmud, which also exhibits various other kinds of abbreviation"
Encyclopaedia Biblica, Rev. T. K. Cheyne D.Litt D.D., J. Sutherland Black M.A. LL.D., Vol. 3, under "Names," p. 3292, item 52 The implication that a descendant of Ishmael would be a major prophet is unacceptable to those Christians who oppose Islam, since the only person to fulfil this description is the prophet Muhammad, peace be upon him. This may explain why Bible scholars assert that the text is referring here to the father of King David (Matthew 1:6). But how likely is it, when describing the pedigree of a man, that reference should be made to an almost unknown person in his family tree (Jesse the father of King David) in preference to a man whose fame has spread across the nations of the earth (Ishmael, the son of Abraham)? It is much more likely that the Jesse of Isaiah 11:10 is Ishmael the son of Abraham, the father of the Arabs, the ancestor of prophet Muhammad.

Firstly, just as a matter of passing interest (to me) but given Muslims' feelings towards the  Bahá'í Faith  perhaps more relevant to them, it  should be noted that Cheyne converted to the Bahá'íst Faith towards the end of his life. It is not surprising therefore to find some of his interpretations supporting Mohammad as a prophet foretold in the Bible (and his wish to belittle the importance of the line of David, since Baha'ists consider David a minor prophet). I certainly admit the Enc Bib is authoritative, but Cheyne's theories regarding names has been thoroughly discredited as far as I can make out. 
"The ingenuity of Cheyne's method may be admitted; but the thesis must be rejected as altogether arbitrary. That it has received serious attention is owing solely to the great service rendered by its sponsor in other departments of Old Testament research.
Cheyne frequently mentions this theory in his Encyclopaedia articles, often appending his view to articles written by people with more mainstream interpretations. He does, however, detail the alternative (and therefore mainstream) views, while doing so. Hence the articles are respected, as long as Cheyne's theory about these names is ignored."
In any case, the Muslim determination to see the shoot of root of Jesse as reference to Mohammad completely fails, as I have pointed out before regarding Deuteronomy, to take into account the context of the rest of Isaiah 11.10. This chapter and the following one are obviously referring to a future glorious end-time when peace rules the Earth and the Jews' political torment is finished (seen any lions eating straw or children playing with snakes recently? do you think knowledge and wisdom cover the Earth since the arrival of Mohammad? and what about the Lord recovering His people from Egypt? or "assembling the dispersed of Israel"?) Still not convinced? Let's look at the next chapter, which as you know is simply a continuation as to what is going to happen when the shoot out of the root of Jesse makes his appearance: 4 And in that day shall ye say: 'Give thanks unto the LORD, proclaim His name, declare His doings among the peoples, make mention that His name is exalted.5 Sing unto the LORD; for He hath done gloriously; this is made known in all the earth.6 Cry aloud and shout, thou inhabitant of Zion, for great is the Holy One of Israel in the midst of thee.' 
Sure, take one verse completely out of context if you wish, ignore the obvious references to the Jewish people, retro-fit names and nick-names - but please don't expect anyone else to swallow it all. 
Finally do Muslim miracle seekers really consider the father of the most important king Israel ever had, to be "almost unknown"? Given the obsession with genealogy*  in the Bible do Muslims really think that fair comment? (Note also the irony of your expecting people to accept the genealogical link between Mary and Aaron despite the thousands of years between them, whilst discounting the relationship between a father and son as unimportant!)
To summarise then: we have the Judeo-Christian Biblical tradition established for millennia which maintains that a direct descendant of King David will be the Messiah. We have Jesse whom no one can dispute is the father of King David.  And we have a verse which states a great prophet will be "a shoot out of the root of Jesse". The verses referring to the root of Jesse also include numerous references to Israel and the Jewish nation. And Muslims maintain this verse, by a strange contraction of the name (why use such a bizarre contraction in a prophesy anyway?) using a discredited method of a follower of the Bahá'í Faith from a century ago, refers to Mohammad. 
How can people believe this utter nonsense?

*According to Genesis 46:12 and Ruth 4:18–22, David is the eleventh generation from Judah, the fourth son of the patriarch Jacob (Israel). The genealogical line runs as follows: (1) Judah → (2) Pharez → (3) Hezron → (4) Ram → (5) Amminadab → (6) Nahshon → (7) Salmon → (8) Boaz (the husband of Ruth) → (9) Obed → (10) Jesse → (11) David