The question seems to be, to me, not just the order of the service but the meaning of the action of the Holy Spirit in Baptism, and then the further action of the Holy Spirit in Chrismation, when Chrismation follows in an order of sequence and is distinct from Baptism.
How are the actions different?
My understanding is that Baptism is a cleansing, regeneration, and grafting into the Church, where Chrismation is a sealing and ordination to the royal priesthood of the believer. Both are done by the Holy Spirit.
I was going to use this passage below in another recently active thread on Baptism but I can use it here just as well. It is one of my favorite catechetical texts concerning Holy Baptism because it is so clear, and so spiritually complete in its expression. I was going to follow up a reflection that I've already posted on Baptism being a grafting of the soul into Christ, or as you say above, into the Body of Christ, the Church.
You can see the claim that is made for Baptism of water below and I think that fits well with what you've said above. Baptism opens us to the Indwelling Trinity, or perhaps better said in this context, Baptism provides that simple singular form in the soul where God is now free to come and go. Where before He could only operate externally to us, now He can dwell within us and give us ever increasing participation in his divine life.
St. Dionysius Areopagite, in his Ecclesiastical Hierarchies
, [PG 3:485], calls the administration of the anointing with chrism τελετη
or making perfect
. This I think comports well also with your understandings, in a more general sense.
And then he also calls Eucharist the deifying mystery and the central sacramental action of the Body of Christ.
78. We share in the image of God by virtue of the intellectual activity of our soul; for the body is, as it were, the soul's dwelling place. Now as a result of Adam's fall, not only were the lineaments of the form imprinted on the soul befouled, but our body also became subject to corruption. It was because of this that the holy Logos of God took flesh, and being God, He bestowed on us thorugh His own Baptism the water of salvation, so that we might be reborn.
We are reborn through water but the action of the holy and life creating Spirit, so that if we commit ourselves totally to God, we are immediately purified in soul and body by the Holy Spirit who now dwells in us and drives out sin.
Since the form imprinted on the soul is single and simple, it is not possible as some have thought, for two contrary powers to be present in the soul simultaneously. For when through holy baptism, divine grace in its infinite love permeates the lineaments of God's image--thereby renewing in the soul the capacity for attain the divine likeness--what place is there for the devil? For light has nothing in common with darkness. [Philokalia, vol 1., St. Diadochos of Photiki, p.280]