Well, at least we agree that it's symbolic, but I really don't know what you mean by "putting on the spirit". And "the soul puts on a physical body". I don't think you understand what a soul is.
I don't think you understand what being a son of God is. I am a soul. I put on a physical body of death at conception. In the near future I will shed Adam's dead corruptible flesh. I will put on God's permanent incorruptible physical body. Then put on the spirit. All spirits reside with God. You can read about them in 1 Kings 22:19-25. None of Adam's offspring has a spirit on over their body. That was taken away and called spiritual death. Death is not just non-existence. Death is separation from God and from being a son of God. Our spirit is not in us. Spirit is not the air we breath, nor the breadth of life.
John at the 5th Seal correctly states how the spirit is put on. The robe of white is symbolic of the spirit. Paul calls it putting on of immortality. The word's root meaning is divinity or about God. God is spirit. So we are putting on spirit.
In the Greek Paul is saying death puts on eternal life. That would be the English form to use, not technically mortal putting on immortality which is the Latin form meaning the same thing. So why do we then call it an immortal body? Paul is not saying we put on a body the second time. Paul states we are putting on eternal life after a body. We are not putting on a body twice. The implication is that the soul is putting on two seperate items. The soul puts on a permanent body and then puts on eternal life separate from the body. But the word immortal should not be used in conjunction with a body. Paul did not use that phrase nor is it ever translated that way. That is personal interpretation turning the word into an adjective and adding the word body. The corruptible to incorruptible already defines the physical. Paul is declaring the spiritual put on over the physical. The spirit is also never able to die. We are separated from the spirit.
The emphasis given throughout Scripture is to avoid all spiritual aspects of life, because those who do are inviting in Satan's demonic world. There is a spiritual presence all around us that we are blind to. That we are given a glimpse in 1 Kings 22 is one of the few places we are allowed to see the spiritual. So Paul is not just saying we put on eternal life, Paul was pointing to the spiritual in distinction to the physical. We are not putting on eternal life as a physical body. We are putting on eternal life as a spiritual body. That is the spirit.
As coming from God, even the Holy Spirit does not go on over the physical body. A demon or spirit is said to enter and indwell the mind, and our thoughts. Just as indicated in 1 Kings 22. However when we are united with our spirit, both John and Paul indicate that the spirit is put on over the body. That is what the symbolism means in Revelation 6.
Now we should see from all examples that no one has their spirit currently in this dead state. The point being is that demons are spirits that have fled from God's presence and are no longer redeemable. There are people who go past the point of redemption into a state of reprobation. Those humans and sons of God prior to the Flood would be examples of those past the point of redemption literally killed by God's judgment. In fact God said His spirit could no longer strive with man's spirit. That is the point a spirit becomes a demon. This process is described for current humanity in Romans 1 by Paul.
If you think you have a soul, then who are you? You certainly are not the body which returns to dust. What would that soul do without you? You are the soul that resides in a physical body of death. You do not have your spirit. Your spirit is with God. Unless one is reprobate, and then their spirit is a demon, which will be cast into the LOF with the soul.
Now you may claim to have a totally different interpretation from Scripture concerning the soul, body, and spirit. Theology has many human opinions on the topic. For one, the Greek word "pneuma" from which we get the word "air" has many different ways it can be used and interpreted. The Latin form became pneumatic. English took both the Greek and Latin to descibe air. One has to go by context.
Paul would not have said we put on air and then assume future generations would understand spirit. Paul was using an euphemism of death putting on non death, to imply the restoration of the spirit. Many just think Paul was repeating himself. Yet they don't follow through and allow us living to be the dead in Christ. We are in death in Paul's euphemism. They don't apply that to living death, they apply that to the physically dead. Those alive are the only ones in death. Those currently in Paradise are in a state of eternal life. They are not the dead in Christ. They are only physically separated from us.
In some context people wrongly claim the spirit leaves the body. In some context the soul is wrongly called spirit. Yet Paul clearly makes the distinction between soul, body, and spirit. And the Greek word for soul as used in modern terms is totally involved with the demonic world. Human understanding does not care for God's Word and the origin of all things being God. Then people complain when I point out Scripture, falsely claiming I am too carnal minded. Then they turn around and frame all their belief on carnal understandings instead of acknowledging the author of all things is God. God created many sons of God on the 6th day, and all were souls in a physical body, within their spirit that was a robe of white, to put it symbolically. Once a spirit is put on, creation will be restored for those souls as originally intended. Death will be no more a separation.