God is quite clear on the subject of Polygamy, it is a violation of his intention in the marriage covenant. But first let me address the verses you cite.
These verses (Ex. 21:10 and Deut. 21:15) provide restrictions on persons who have more than one wife, but they do not promote or support having more than one wife. You must understand the logical distinction between these two concepts. Consider that American has laws that provide restrictions on how much alcohol you can drink. But this does not itself mean that America promotes drinking alcohol.
Or consider Jesus' example of divorce. The OT Law provided restrictions on divorce. But clearly God did not promote divorce. In fact, God hates divorce. Yet he did not make a ban of divorce a civil/judicial issue. Rather, he places lesser civil/judicial restrictions on divorce. This simply means that the civil law is not identical to the moral law (this should be obvious, really) and that no immediate inference can be made from civil law to moral law.
So the verses you have given us which provide restrictions on polygamy do not prove that God looks favorably on polygamy any more than divorce law restrictions prove that God looks favorably upon divorce.
But that God looks down upon polygamy is clear throughout the Genesis narrative, including the account of God creating just one woman for Adam. As OT scholar Gordon Wenham states,
"...it is striking that the LORD God created only one Eve for Adam. Polygamy was an accepted feature of life in ancient Israel especially among the leaders of society, yet Adam is provided with just one wife. This is not meanness on God’s part, for the rest of the story shows him keen to supply Adam’s every need, and Adam’s shout of greeting when he meets Eve shows he is perfectly satisfied with just one wife.
That's a straw man since it's not implied that every man desires polygamy. On the contrary, although there are many examples of polygamy in scripture, most marriages were monogamous.
The rest of Genesis seems to confirm monogamy as the most desirable situation, as all the polygamous marriages it describes are marred by strife.
Correlation doesn't imply causation.
Finally, had Adam been supplied with several wives, he could have been fruitful and multiplied even quicker! The creation of one Eve thus shows that monogamy is more important than rapid multiplication…
No it doesn't. Non-sequiter.
Lamech, the first bigamist, is a vicious thug, boasting that he will take seventy-sevenfold vengeance on those who attack him (4:23–24).
More confusion of correlation and causation.
Sarah’s resort to surrogate motherhood, though a well-known practice in the ancient Near East, is described in terms that echo Genesis 3 and causes great tension between Sarah, Hagar and Abraham.
This isn't a good example since the only sense in which it was polygamy was for the specific purpose of bearing a child. It was polygamy for a the sake of bearing a child, not polygamy for its own sake.
Jacob’s involuntary bigamy leads to a most unhappy marriage for all concerned. As Leah and Rachel name their sons, they pour out their feelings of rejection on the one hand and their desire for more children on the other (29:32–30:24)."
As mentioned above, it wasn't claimed that polygamy is for everyone. The fact a person dislikes something doesn't imply that it's universally wrong, and for that matter doesn't even necessarily imply that it's wrong for that particular person.
(Story as Torah: Reading Old Testament Narrative Ethically. 31-33)
Even prior to the NT being written, there were Jews who recognized that polygamy is a sin and they often made their argument by "glossing" Genesis 2:14 with the word "two" instead of "they." This is justifiable since God only made Adam and Eve, but it's also obviously meant to be normative insertion of the narrator, explaining the institution of marriage. This is the background to Jesus' statement in Matthew 19 (and Mark 10) that "...the two shall become one flesh’... So they are no longer two but one flesh" (vss 5-6). In other words,
The significant point, as far as the Gospel text [Matthew 19] is concerned, is that this variant text is used very self-consciously, with the additional comment 'So they are no longer two but one' emphasizing the presence of the word 'two.'... This type of exegesis was common in early rabbinic Judaism and was later called gezerah shavah… This exegesis would have been obvious to any intelligent listener and was not normally accompanied by any kind of explanation when it occurred in rabbinic literature or in the Targums. The frist text, Genesis 1:27, was part of a standard proof for monogamy as seen in the Damascus Document... Both Mark and the Damascus Document cite exactly the same portion of Genesis 1:27, and they both precede the quotation with a very similar phrase. Mark refers to 'the beginning of creation'... while the Damascus Document used the phrase 'the foundation of creation'... they are semantically identical.... Jesus was making the point very strongly. He was saying not only that polygamy was immoral but that it was illegal.
(David Instone-Brewer. Divorce And Remarriage In The Bible. 137-138)
20 So Adam gave names to all cattle, to the birds of the air, and to every beast of the field. But for Adam there was not found a helper comparable to him. 21 And the Lord God caused a deep sleep to fall on Adam, and he slept; and He took one of his ribs, and closed up the flesh in its place. 22 Then the rib which the Lord God had taken from man He made into a woman, and He brought her to the man. 23 And Adam said: "This is now bone of my bones And flesh of my flesh; She shall be called Woman, Because she was taken out of Man." 24 Therefore a man shall leave his father and mother and be joined to his wife, and they shall become one flesh. (Genesis 2:20-24)
1 Now it came to pass, when Jesus had finished these sayings, that He departed from Galilee and came to the region of Judea beyond the Jordan. 2 And great multitudes followed Him, and He healed them there. 3 The Pharisees also came to Him, testing Him, and saying to Him, "Is it lawful for a man to divorce his wife for just any reason?" 4 And He answered and said to them, "Have you not read that He who made them at the beginning 'made them male and female,' 5 and said, 'For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh'? 6 So then, they are no longer two but one flesh. Therefore what God has joined together, let not man separate." 7 They said to Him, "Why then did Moses command to give a certificate of divorce, and to put her away?" 8 He said to them, "Moses, because of the hardness of your hearts, permitted you to divorce your wives, but from the beginning it was not so. 9 And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery." 10 His disciples said to Him, "If such is the case of the man with his wife, it is better not to marry." 11 But He said to them, "All cannot accept this saying, but only those to whom it has been given: 12 For there are eunuchs who were born thus from their mother's womb, and there are eunuchs who were made eunuchs by men, and there are eunuchs who have made themselves eunuchs for the kingdom of heaven's sake. He who is able to accept it, let him accept it." (Matthew 19:1-12)
1 Now it came to pass, when Jesus had finished these sayings, that He departed from Galilee and came to the region of Judea beyond the Jordan. 2 And great multitudes followed Him, and He healed them there. 3 The Pharisees also came to Him, testing Him, and saying to Him, "Is it lawful for a man to divorce his wife for just any reason?" 4 And He answered and said to them, "Have you not read that He who made them at the beginning 'made them male and female,' 5 and said, 'For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh'? 6 So then, they are no longer two but one flesh. Therefore what God has joined together, let not man separate." 7 They said to Him, "Why then did Moses command to give a certificate of divorce, and to put her away?" 8 He said to them, "Moses, because of the hardness of your hearts, permitted you to divorce your wives, but from the beginning it was not so. 9 And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery." 10 His disciples said to Him, "If such is the case of the man with his wife, it is better not to marry." 11 But He said to them, "All cannot accept this saying, but only those to whom it has been given: 12 For there are eunuchs who were born thus from their mother's womb, and there are eunuchs who were made eunuchs by men, and there are eunuchs who have made themselves eunuchs for the kingdom of heaven's sake. He who is able to accept it, let him accept it." (Mark 10:1-12)
Jesus said that "a man" and "his wife" are "two." The claim that reference to "a man" and "his wife" as "two" is a prohibition against polygamy is simply not in the text, nor is it implied.
8 Beware lest anyone cheat you through philosophy and empty deceit, according to the tradition of men, according to the basic principles of the world, and not according to Christ. (Colossians 2:8)
8 "For laying aside the commandment of God, you hold the tradition of men--the washing of pitchers and cups, and many other such things you do." (Mark 7:8)
"[A] man" and "his wife" are indeed "two." That doesn't imply that a man may not have more than one wife; he's referring to "the two [becoming] one flesh." Since this can only happen at any one time between one man and one woman, the only number of people it makes sense to refer to here is "two," regardless of how many wives the man in question may have. In context, the "two" people being referred to are not the total number of people in a marriage, but rather the total number of people "[becoming] one flesh."