Wrong.
As you point out, there are other occurrences of the word "adoption" and not all of them mean or refer to the same thing.
You are hanging your understanding on only one usage, and in doing so, you are, essentially, hanging yourself.
You have stated: " Usually our adoption refers to our physical resurrection at the second coming of Christ" This is not correct.
Paul uses the word υἱοθεσία five times:
1. Romans 8:15
[12] So then, brothers, we are debtors, not to the flesh, to live according to the flesh. [13] For if you live according to the flesh you will die, but if by the Spirit you put to death the deeds of the body, you will live. [14] For all who are led by the Spirit of God are sons of God. [15] For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!” [16] The Spirit himself bears witness with our spirit that we are children of God, [17] and if children, then heirs—heirs of God and fellow heirs with Christ, provided we suffer with him in order that we may also be glorified with him. (Romans 8:12-17 ESV; emphasis mine)
In verse 15, "adoption" is preceded by the verb "have received." This is an Aorist verb, indicating the "reception" of adoption happened in past time. The event, the adoption, is seen in its totality. There is no hint of a "future" adoption here.
2. Romans 8:23
[18] For I consider that the sufferings of this present time are not worth comparing with the glory that is to be revealed to us. [19] For the creation waits with eager longing for the revealing of the sons of God. [20] For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope [21] that the creation itself will be set free from its bondage to corruption and obtain the freedom of the glory of the children of God. [22] For we know that the whole creation has been groaning together in the pains of childbirth until now. [23] And not only the creation, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for adoption as sons, the redemption of our bodies. [24] For in this hope we were saved. Now hope that is seen is not hope. For who hopes for what he sees? [25] But if we hope for what we do not see, we wait for it with patience. (Romans 8:18-25 ESV; emphasis mine)
In this instance, Paul does indeed relate "adoption" to the redemption of our bodies. However, to say that is the sum-total of adoption is to do violence to this text and the other usages.
You completely discount that Paul, only a matter of words earlier, states: "we ourselves...have the firstfruits of the Spirit..." Paul is clearly talking about "firstfruits" here as relating to "adoption." What is the indicator of our coming adoption? We have
already been given the Spirit. So, it cannot be, textually or otherwise, that adoption is confined only to the redemption of our bodies.
Truly, we "already" have adoption and we have "not yet" been adopted. But, this will become clear as we press on to view uses 3-5.
3. Romans 9:4
I am speaking the truth in Christ—I am not lying; my conscience bears me witness in the Holy Spirit—[2] that I have great sorrow and unceasing anguish in my heart. [3] For I could wish that I myself were accursed and cut off from Christ for the sake of my brothers, my kinsmen according to the flesh. [4] They are Israelites, and to them belong the adoption, the glory, the covenants, the giving of the law, the worship, and the promises. [5] To them belong the patriarchs, and from their race, according to the flesh, is the Christ, who is God over all, blessed forever. Amen. (Romans 9:1-5 ESV; emphasis mine)
In this passage, Paul is clearly stating that the Israelites have
already been "adopted," so to speak. He is referencing the Corporate Election of the Old Testament. This is not something Israel is waiting for; they already have it. Now, of course, Paul is not here equating adoption with salvation. But, the usage here of the word "adoption" is not eschatalogical. Rather, it is an existent reality--The Nation of Israel has been adopted by God (though they, obviously, failed to live up to all that this adoption required of them).
4. Galatians 4:5
I mean that the heir, as long as he is a child, is no different from a slave, though he is the owner of everything, [2] but he is under guardians and managers until the date set by his father. [3] In the same way we also, when we were children, were enslaved to the elementary principles of the world. [4] But when the fullness of time had come, God sent forth his Son, born of woman, born under the law, [5] to redeem those who were under the law, so that we might receive adoption as sons. [6] And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!” [7] So you are no longer a slave, but a son, and if a son, then an heir through God. (Galatians 4:1-7 ESV; emphasis mine)
In this passage, which is quite enlightening, Paul clearly states that adoption is the result of Christ's work of redemption. In other words, Christ died so that we could, indeed, be adopted by God. Now, the grammar views the "adoption" as a single event, likely in the past (hence the Aorist Subjunctive). But, the Aorist shouldn't be pushed too far.
But, we really don't need to dissect the grammar here to understand that the adoption has already taken place. Paul clearly calls the believers in Galatia "sons." So, the adoption has already taken place. Further evidence of the adoption having already taken place is given in the following verses where Paul clearly states "You...are a son...[and] an heir." The Present Active Indicative of the verb "to be" here tells us that the "adoption" is a present reality, it is not something reserved for the far off future.
5. Ephesians 1:5
[3] Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, [4] even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love [5] he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will, [6] to the praise of his glorious grace, with which he has blessed us in the Beloved. [7] In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, [8] which he lavished upon us, in all wisdom and insight [9] making known to us the mystery of his will, according to his purpose, which he set forth in Christ [10] as a plan for the fullness of time, to unite all things in him, things in heaven and things on earth. (Ephesians 1:3-10 ESV; emphasis mine)
This passage makes it absolutely clear that "adoption" is something that is a result of God's sovereign choice and His predestining persons to be "adopted." The language here, especially, shows that we are indeed set apart by adoption. It is the present adoption of believers that is a result of God's plan. Adoption does not bring election; election brings adoption.
So, while you may be right that there is an eschatological understanding of "adoption," it is certainly not the only use of the word.
Paul's five uses make quite clear what many of the great theologians have already pointed out: Those who are believers are
already adopted even as they are
not yet adopted.
This tension between the "Already" and "Not Yet" is important and difficult. Yet Paul's usage make it absolutely clear that this is what he has in mind: An "already" adoption waiting for a fuller, "not yet" adoption.
The Archangel