What I've found so interesting is the difference we tend to see here, and in other forums of this kind where we have so much opposition to our belief in the Godhead, compared to what I've encountered with most of the non-LDS Christians I've personally known.
I would have to say most of them have not had need to further resolve anything either, having views much more closely aligned to LDS belief than not, which they have based on Biblical scripture.
I've given examples here in the past, though mostly what I received in response by non-LDS was that those I used in example must not know, understand, or believe in the teachings of their various faiths. So, go figure.
As for myself, I have had no need to accept the explanations of others on the matter of the Godhead, and it is not because of Joseph Smith that I've not had need to resolve anything further. With the beautiful simplicity of the scriptural record in this matter, I've never found the need.
Here's an example of one of the times I attempted to explained the LDS perspective to someone who claimed LDS were not Christians because, he said, we did not worship the "One True God of the Bible" because we had a different belief regarding the Godhead, than the one he held:
There is only, "One God and Father of all." This is the One True God of the Bible. There is only one Lord and Savior, who is Jesus Christ. He is God's Son. And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. (John 17:3)
God the Father is the First member of the Godhead. Jesus Christ, who is our Savior, is the second member of the Godhead. The Holy Ghost is the third member of the Godhead. As members of the Godhead, each of these three individuals have the title of God, but God The Father holds preeminence, He being the Supreme Ruler of the Universe, The Great and Almighty God. The Highest, and the Father of all. "The One True God."
It is His work that both the Son and the Holy Ghost do. They speak, act, testify, and bear witness of Him in all things, therefore they do the work of, "The One True God." It is He they serve, not themselves. All teachings and commandments of God ever given to man, come from "The One True God," God the Father, whether He speaks the words Himself, or Christ speaks His words, or the Holy Ghost testifies to them.
All doctrines, whether spoken by the Father's own mouth, or through the mouth of His Son, Jesus Christ, come from the Father, "The One True God." All truths that the Holy Spirit bears witness of to man, come from the mind and will of the Father, "The One True God."
Therefore, even though they are three distinct and separate individuals, they are One God, being One Godhead, as there is only, "One True God," whose work they do. Jesus was sent by Him, and is subordinate to Him, as is the Holy Ghost, who bears witness of God the Father, and of His Son, Jesus Christ, as the Savior of the world. Jesus did not do his own will, but the will of God, his Father, in all things, with his Father, being, "The One True God."
God the Father is our God. Jesus Christ is our Lord and Savior. Jesus is the author and finisher of our faith and our salvation. He suffered, bled, and died for us, so that we, through him, might come unto God the Father and gain eternal life. Therefore, Jesus Christ, whom we praise and adore as Lord, God, and King, is the very center of our faith, and our reverence for what he did for us is beyond measure.
However, we follow Our Savior's example and teachings in our worship of God. We worship the same God that Jesus worshiped, the same God he taught us to worship. We pray to the same God that Jesus prayed to, the same God he taught us to pray to, and we ask all things of God the Father, in Jesus' name, just as Jesus taught, and believe in only, "One God and Father of all, who is above all, and through all, and in you all." (Ephesians 4:6)
We also echo Paul's teaching, that, "For though there be that are called gods, whether in heaven or in earth, (as there be gods many, and lords many,) But to us there is but one God, the Father, of whom are all things, and we in him; and one Lord Jesus Christ, by whom are all things, and we by him." (1 Corinthians 8:5-6)
This does not mean we exclude the other members of the Godhead from worship, because, by the very definition of the word, our worship encompasses them all. But, in the most strict sense of worship, ours is reserved for the God our Lord and Savior taught us to worship, He being God, Our Father.
Hope that helped.
But, maybe there are those who cannot see the simplicity of that. Or maybe there are those who need God to be more of a mystery. I don't know.