Who was Jesus the Christ

The use of the word God:
First an understanding is in order one you even stated quite clearly. The word Elohim/God is a title it isn't a unique designation of an individual.

The Book of Mormon is completely consistent in its doctrine of the Godhead and the nature of God. It denies Modalism and that God is a single person who has revealed himself in three modes or forms.
For it is absolutely clear.
Jesus Christ is an individual person who is the Son of another individual person.
The Father of Jesus Christ is someone different than he is but is an individual person.
The word God isn't a unique designation of an individual but is a title Elohim/God.
The idea of being a father of a person is symbolic and literally understood.

Jesus Christ is the literal son conceived in the flesh who dwell as a man upon the earth.

His father a different individual conceived him.

Jesus the Christ is the father symbolically and they are accounted his seed to all them that accept his covenants, and are called after his name.

Jesus the Christ is the father of heaven and earth having been the predominant individual involved in their organization.

Who is Jesus Christ?

How Jesus Christ is the Son:
He is the Son of the Living God an Elohim who conceived him through his power.
He is the Son because he took upon him flesh and suffered the will of the father being subject to the flesh.
He is the Son because he suffered hunger, pain, sleepiness, anguish of spirit, and soul, and body
He is the Son because he suffered temptations the same as any man - and never once succumbed...
He is the Son because he experienced a veil of forgetfulness as all mankind - and was tempted, tried, and was triumphant over the flesh.
He is the Son being subject to the flesh, being tempted in the flesh, and yet always doing the will of the Father.
His name is Jehovah - the God of Abraham, and Isaac, and of Jacob - who before he was born visited and spoke with these individuals.
He is the Elohim of Abraham, and of Isaac, and of Jacob - who was lifted up, and crucified, and lain in a sepulcher
He is the Redeemer and the Messiah - who redeems and saves all mankind from death and hell, he is the Holy one of Israel.
He is the Son who became the author of Eternal salvation unto all them that obey him.

How Jesus Christ is the Father:
He is the Father because he was conceived by the Power of Elohim - The Father of all spirits Elohim.
He is the Father because all mankind as they accept him as their savior and take upon them his name - are called his seed, and are spiritually begotten as his children.
For all redeemed individuals, and exalted individuals are accounted his seed, they are his.
He is the Father who was the Elohim of Abraham, who was the creator and the redeemer of all mankind. For he is the Father of heaven and earth - having created them.
How Jesus Christ is one with his Father - who both have the title of Elohim/God/Judge and ruler - the perfectness of lights...
They are both the fathers of the children of men who repent and come unto him. Elohim the Father because he organized their spirits. Jesus/Jehovah because they enter into a covenant relationship with him and become his sons and daughters taking upon them his name and being called under his head. For they are accounted his seed.
He is one with his father in purpose, in mind, and in the things that he does. For he only does what he has seen his father do.
Thus the Book of Mormon is completely consistent in it's doctrine of the Godhead and the nature of God. Rather it seems inconsistent to those who do not have a correct understanding of his characteristics and attributes, thus they are confused and are brought under bondage, not knowing what and who they worship.
It denies Modalism - and teaches the truth of the Godhead. Three separate and distinct individuals with different characteristics but the same goal/purpose and plan.
The father - being a resurrected and immortal being - an Elohim - with a physical celestial body.

Jesus Christ a separate person:
The son - being initially a spirit and as a spirt was the Elohim of Abraham, Isaac, and of the Old Testament.
The son - being born of a woman, taking upon him flesh as any man, being subject to temptations, pain, suffering, anguish, sadness, tiredness, hunger and fatigue.
The son - becoming the author of eternal salvation unto all them that obey him. Growing, developing, learning and being perfected by his father through the plan of salvation.
The son - being a father - being the redeemer of all mankind and their spiritual father, they being accounted his seed, taking upon them his name and glorifying him through their progression.
The son - being a father - being the creator of heaven and earth and all physical things therein.
The son - being glorified of the father - he received of his father the power to live again, all power in heaven and earth, an immortal and resurrected body, and he became the author of eternal salvation to all of the father's children given into his power.
It totally blows Modalism out of the water in all respects - and teaches that it is a heresy and denies the nature and characteristics of God.