Paul is describing different things.
(All verses KJV)
Exegesis of 1 Corinthians 15:17-28
In 1 Cor 15, Paul starts talking about the resurrection -- the 'hope'.
15.17-20 And if Christ be not raised, your faith is vain; ye are yet in your sins...If in this life only we have hope in Christ, we are of all men most miserable. But now is Christ risen from the dead, and become the firstfruits of them that slept.
When you see "firstfruit", you always think of the resurrection. The first fruit was the first of the barley harvest, lifted up to God on the day after the Sabbath (Sunday).
v21-23 For since by man came death, by man came also the resurrection of the dead. For as in Adam all die, even so in Christ shall all be made alive. But every man in his own order: Christ the firstfruits; afterward they that are Christ’s at his coming.
We are still talking about the resurrection. Christ was the first to be harvested and we will be resurrected with him.
Who will be resurrected? "They that are Christ's".
When? "At his coming". Thus we are talking about the Eschaton
v 24 Then cometh the end, when he shall have delivered up the kingdom to God, even the Father; when he shall have put down all rule and all authority and power.
"Put down" = καταργέω. It has the sense of inactivate. Or abolish. Or set aside. It is used in
1 Cor 6.13: Meats for the belly, and the belly for meats: but God shall destroy [καταργέω] both it and them.
1 Cor 13:10 But when that which is perfect is come, then that which is in part shall be done away [καταργέω]
1 Corinthians 2:6 Howbeit we speak wisdom among them that are perfect: yet not the wisdom of this world, nor of the princes of this world, that come to nought:[καταργέω]
So at the Eschaton, when the bride is complete and the harvest is finished, all rule and authority shall be abolished.
v25 For he must reign, till he hath put all enemies under his feet.
This is now. He is reigning now. It is a quote from a Psalm 110:1
The LORD said unto my Lord,
Sit thou at my right hand,
Until I make thine enemies thy footstool.
So until his enemies are put under his feet, Christ is reigning, sitting at the right hand of God. What event is referred to by this instance of "put the enemies under his feet"?
Here "put" = τίθημι and it means to place or set, and it is not the same language used in verse 28. Right now, there is opposition. There is suffering, testing, trials. Christ suffered as the head, but the body (his bride) must also suffer:
Col 1.24: Who now rejoice in my sufferings for you, and fill up that which is behind of the afflictions of Christ in my flesh for his body's sake, which is the church:
Right now, the faith is being tested and proven:
1 Peter 1.7: That the trial of your faith, being much more precious than of gold that perisheth, though it be tried with fire, might be found unto praise and honour and glory at the appearing of Jesus Christ:
This suffering is caused by opposition. Satan has been cast into the earth and he opposes the saints. However this is all to serve God's purpose. God sets the amount and the times of our testing, so that the Bride will be brought forth, fully tested, just as Christ was fully tested in his earthly life.
Thus the opposer is still subject to Christ Just as Pharaoh (in his mind) was the enemy of Israel, but in God's mind was just an instrument of opposition.
However there will come a time when Satan will be "deactivated" by being thrown at Christ's feet (e.g. placed at his feet). Think of a bound prisoner being carried into the throne room and laid at the foot of the king. That marks the end of the opposition, which will happen at the Eschaton.
This picture of the prisoner being placed at the feet of the king is what is meant by "For he must reign, till he hath put [placed] all enemies under his feet."
v26 The last enemy that shall be destroyed is death.
When there is no more need for testing and suffering, there will be no more need for death. The Eschaton would have arrived. So this will happen in the future.
Now we shift back to the present:
v27 For he hath put all things under his feet. But when he saith, all things are put under him, it is manifest that he is excepted, which did put all things under him.
Here, "put" = "subjugate" = ὑποτάσσω. BDAG: to cause to be in a submissive relationship, to subject, to subordinate
So right now the opposer is submissive to Christ, because Christ is in charge by being elevated above him. It is important to understand that Christ is the one who is ultimately responsible for our suffering, just as the Father was ultimately responsible for the suffering of the son. This is a key point in Job. God is the behind the scenes, causing everything to happen. Satan is merely Christ's instrument. God threw the devil into the earth, in order to be the opposition, so that the body of Christ can be filled up with the suffering that it lacks.
Acts 9.16: For I [Jesus] will shew him [Paul] how great things he must suffer for my name's sake.
Exodus 9.16: And in very deed for this cause have I [God] raised thee up, for to shew in thee [Pharaoh] my power; and that my name may be declared throughout all the earth.
Job 1.8a: ...Hast thou considered my servant Job?
If you think suffering is strange and not in God's plan -- if you have a theology of glory instead of a theology of the cross, then you will think that Christ isn't reigning and some things are not subject to him, and you will start inventing theologies to explain how things aren't what they should be. This is why people always think God will reign in the future, but cannot imagine him reigning now, just as they imagine going to heaven in the future but not being in heaven now (even though Paul says we are already dead and our lives are hid with Christ in God). Because now there is suffering and people think the suffering somehow opposes God's will, when really the suffering is to create the trial of our faith that is more precious than gold.
But in Paul's theology, everything is exactly how it should be right now and it is all subject to Christ right now. It's just that the category of "should be" includes stuff like Christ dying on the cross and ourselves suffering.
However once the Eschaton hits and the bride is complete, adorned with all the gold that is required, that opposer will be abolished. He will be taken out of the earth and placed at Christ's feet. It is very sad that Paul had to use the "under the feet" phrase to describe both of these events, but a careful reader can see distinctions that don't involve "changes in timing".
v 28 And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him, that God may be all in all.
"him" refers to the Father, not Christ. Another distinction is being made here.
Right now, the Son reigns, and everything is subject to the Son. But the opposer, who is subject to the Son, is running around the earth doing the Son's will, but not immobilized at the Son's feet.
When the opposer's work is complete, he will then be taken out of the earth and placed at Christ's feet, then the opposer and death will be abolished. Then the Son will hand over all subjection to the Father, and will himself become subject to the Father. Thus this is again the Eschaton and refers to the future.
Exegesis of Ephesians 1:19-23
Once we understand that suffering is not strange but is necessary, and that God is in control of everything including our suffering, then everything becomes obvious, so I will go through this quickly.
v 19–21 And what is the exceeding greatness of his power to us-ward who believe, according to the working of his mighty power, Which he wrought in Christ, when he raised him from the dead, and set him at his own right hand in the heavenly places, Far above all principality, and power, and might, and dominion, and every name that is named, not only in this world, but also in that which is to come:
So Christ is already reigning (which we saw) and everything is already subject to him (which we also saw). Here Paul adds the wrinkle that this is not only now, but "in the world to come". I would like to avoid doctrinal discussions about the world to come, so I'll move on.
v 22 And hath put all things under his feet, and gave him to be the head over all things to the church, which is his body, the fulness of him that filleth all in all.
Again with the feet. Fortunately "put" is again "ὑποτάσσω" so this refers to everything being subject to Christ. Satan is still running around testing the faith of the saints and causing suffering so he is not immobilized at the feet, but he is subject to the feet. The reference to the Church as "his body" is perhaps a subtle hint that as Christ had to be crucified to demonstrate his obedience to the Father, the church will also suffer as it is his body.
We are done. Paul is not hard to read once you accept a few key ideas, like Col 1.27 "Christ in you, the hope of Glory", as well as the theology of the cross. But the theology of the cross underpins all.