Ontological identity of the Logos with God would mean that Jesus is also the Father, which Trinitarianism claims to reject.
Again, you don't understand the Trinity doctrine. In particular, you are confused about the difference between immanent trinity (the triune God before creation) and economic trinity (post creation). When John 1:1 refers to the relationship of God and the Word in the beginning, it speaks of immanent trinity. It has nothing to do with Jesus born to Mary (economic trinity). You're right, the church rejects the heresy that the Father became the bleeding Son on the cross, that the father became the son; this is the lie that the Jehovah's Witnesses continue to spread, that this is what real Christians believe, but that is not mainstream teaching. That is the heresy of patripassianism. John 1:1c isn't claiming to say that the Word was Jesus. That is simply not true and mischaracterizes the issue.
But in fact, if the Logos is the same in every way with the Being described as God in the Bible, then "the Word is God" can only mean that the Word is the Father.
More confusion. You have to ask in what sense they are equal. God the Son and God the Father are equal with respect to divinity, power and nature.
There is subordination of relation and order among the three Persons, but not in nature:
Moreover, the subsistence and operations of the three Persons are marked by a certain order involving a certain subordination in relation, though not in nature. The Father as the fount of deity is First: He is said to originate. The Son, eternally begotten of the Father, is Second: he is said to reveal. The Spirit, eternally proceeding from the Father and the Son, is Third: He is said to execute.
While this does not suggest priority in time or in dignity, since all three Persons are divine and eternal, it does suggest an order of precedence in operation and revelation. Thus we can say that creation is from the Father, through the Son, by the Holy Spirit. (New Bible Dictionary, 1299, 1300)
Each Person has the divine nature, but each has it differently:
Whatever is other, distinct, plural, personal, and proper in the Godhead is exclusively a matter of relationship. Father, Son and Spirit do not differ as God, but in the way each is God with respect to the others. Each has and is the divine nature, but each has it differently: the Father from Himself, the Son from the Father, the Spirit from both the Father and the Son. God, then, is one in substance, three in Person, and what is significant about this distinction, what makes it non-contradictory, is that what is personal in the Godhead is not something absolute, but something purely relative, (Council of Florence, 1442). (Catholic Encyclopedia, 303)
The doctrine also holds that the divine Persons exist in their relationships to one another:
The three divine Persons exist in their particular, unique natures as Father, Son and Spirit in their relationships to one another, and are determined through these relationships. It is in these relationships that they are Persons. Being a person in this respect means existing-in-relationship. (Trinity and the Kingdom, 172)
[T]he three divine Persons possess the same individual, indivisible and one divine nature, but they possess it in varying ways. The Father possesses it of himself; the Son and the Spirit have it from the Father (ibid., 172). The Trinitarian Persons subsist in the common divine nature; they exist in their relations to one another. (ibid., 173)
“A divine Person is a non-interchangeable existence of the divine nature.” By the word ‘existence’ - existential - [he] meant: existence, in the light of another” (ibid., 173).
http://144000.110mb.com/trinity/index.html
As a matter of fact, the view which the Jehovah's Witnesses ascribe to Trinitarians - the exaggerated view of Noetus which identified “Christ with the Father,” was rejected by the church many centuries ago along with similar heretical distortions (Catholic Encyclopedia, 296).
In its extreme form it may suggest that the whole of God was, for example, present in Jesus - that heaven was empty when Jesus walked on earth. In relation to the cross, it may imply that, because there is no distinction between Father and Son, the whole of God suffers equally as Jesus dies, and indeed God dies entirely on the cross …. (Oxford, 1211)
This and similar notions are precisely some of the “pitfalls” the “doctrine of the Trinity sets out to avoid …” (Oxford, 1211). Any implications or explicit assertions by the Jehovah's Witnesses to the contrary are untrue - they are false accusations.