"I've heard that Jesus never actually claimed He was God."

John 14:7-10 [7] If you really knew me, you would know my Father as well. From now on, you do know him and have seen him." [8] Philip said, "Lord, show us the Father and that will be enough for us."   [9] Jesus answered: "Don't you know me, Philip, even after I have been among you such a long time? Anyone who has seen me has seen the Father. How can you say, `Show us the Father'?  [10] Don't you believe that I am in the Father, and that the Father is in me? The words I say to you are not just my own. Rather, it is the Father, living in me, who is doing his work.

John 10:30  "I and the Father are one."

John 14:11  Believe me when I say that I am in the Father and the Father is in me; or at least believe on the evidence of the miracles themselves.

John 10:37-38 [37] Do not believe me unless I do what my Father does. [38] But if I do it, even though you do not believe me, believe the miracles, that you may know and understand that the Father is in me, and I in the Father."

Matthew 27:43 He trusts in God. Let God rescue him now if he wants him, for he said, 'I am the Son of God.'"

John 17:11   I will remain in the world no longer, but they are still in the world, and I am coming to you. Holy Father, protect them by the power of your name--the name you gave me--so that they may be one as we are one.

"When Jesus said 'I and the Father are one' didn't He just mean they are of one accord, they are merely like-minded?"

Considering the overall content of the Bible, this cannot be:

The Greek word he used, heis, is the word for the number one. It is a reference to the Shema, the core tenet of Judaism, "Sh'ma, Yisrael, Adonai Eloheynu Adonai echad," which, using Christian terminology is, "Hear, O Israel, Jehovah is our God. Jehovah is one."

John 10:31-33  [31] Again the Jews picked up stones to stone him, [32] but Jesus said to them, "I have shown you many great miracles from the Father. For which of these do you stone me?"   [33] "We are not stoning you for any of these," replied the Jews, "but for blasphemy, because you, a mere man, claim to be God."

John 17:5  And now, Father, glorify me in your presence with the glory I had with you before the world began.

John 17:10   [Speaking to the Father] All I have is yours, and all you have is mine. And glory has come to me through them.

Note: "Son of Man" was a term referring to the expected Messiah.

Mark 14:61b-62   [61b] Again the high priest asked him, "Are you the Christ, the Son of the Blessed One?"  [62] "I am," said Jesus. "And you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven."

Luke 22:66-70  [66] At daybreak the council of the elders of the people, both the chief priests and teachers of the law, met together, and Jesus was led before them. [67] "If you are the Christ, " they said, "tell us."  Jesus answered, "If I tell you, you will not believe me, [68] and if I asked you, you would not answer. [69] But from now on, the Son of Man will be seated at the right hand of the mighty God."  [70] They all asked, "Are you then the Son of God?"  He replied, "You are right in saying I am."

Daniel 7:13-14 [13] "In my vision at night I looked, and there before me was one like a son of man, coming with the clouds of heaven. He approached the Ancient of Days and was led into his presence. [14] He was given authority, glory and sovereign power; all peoples, nations and men of every language worshiped him. His dominion is an everlasting dominion that will not pass away, and his kingdom is one that will never be destroyed.
 

Jesus clearly and repeatedly indicated that He is not the one who "calls the shots".

John 14:31  the world must learn that I love the Father and that I do exactly what my Father has commanded me.

John 7:16 Jesus answered, "My teaching is not my own. It comes from him who sent me."

John 8:42  Jesus said to them, "If God were your Father, you would love me, for I came from God and now am here. I have not come on my own; but he sent me."

John 17:3-12   [3] Now this is eternal life: that they may know you, the only true God, and Jesus Christ, whom you have sent. [4] I have brought you glory on earth by completing the work you gave me to do. [5] And now, Father, glorify me in your presence with the glory I had with you before the world began. [6] I have revealed you to those whom you gave me out of the world. They were yours; you gave them to me and they have obeyed your word. [7] Now they know that everything you have given me comes from you. [8] For I gave them the words you gave me and they accepted them. They knew with certainty that I came from you, and they believed that you sent me. [9] I pray for them. I am not praying for the world, but for those you have given me, for they are yours. [10] All I have is yours, and all you have is mine. And glory has come to me through them. [11] I will remain in the world no longer, but they are still in the world, and I am coming to you. Holy Father, protect them by the power of your name--the name you gave me--so that they may be one as we are one. [12] While I was with them, I protected them and kept them safe by that name you gave me. None has been lost except the one doomed to destruction so that Scripture would be fulfilled.
  

The Hebrew Bible
(Old Testament)
Says God Has A Son

From The Tanakh -- The New JPS Translation
(c) 1985 by the Jewish Publication Society

Proverbs 30:4 [JPS]

Who has ascended heaven and come down?
Who has gathered up the wind in the hollow of his hand?
Who has wrapped the waters in his garment?
Who has established all the extremeties of the earth?
What is his name or his son's name, if you know it?

Proverbs 30:4 [NKJV]   Who has ascended into heaven, or descended?  Who has gathered the wind in His fists? Who has bound the waters in a garment? Who has established all the ends of the earth? What is His name, and what is His Son's name, if you know?

THE HEBREW BIBLE (THE OLD TESTAMENT) SAYS THAT GOD WOULD COME TO EARTH AS A HUMAN MALE.

Isaiah 9:6-7 [6] For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. [7] Of the increase of his government and peace there will be no end. He will reign on David's throne and over his kingdom, establishing and upholding it with justice and righteousness from that time on and forever. ...

When Jesus claimed to be God incarnate, either:

1. He was telling the truth.
2. He was lying -- He wasn't God and knew it.
3. He was a lunatic -- He wasn't God but thought He was.

This is known as The Trilemma.