Here are a few things to consider as to why Paul mostly uses the term Christ Jesus.
First of all when he met him on the Damascus Road he met the ascended glorified Christ Jesus. He never knew him after the flesh like the 12 apostles.
A.E. Knoch (1874-1965):
"Christ Jesus"and "Jesus Christ"-What a vast difference between these two titles, though one is merely a transposition of the other!
"Jesus Christ "is the humble, despised, rejected, crucified Messiah. His glorious wait until the future, at the time of His return to earth. At present He has no place down here. But "Christ Jesus" Already He is highest in the heavens. Seated at the right hand of God, there is no dignity to equal His. .... His present place of power and sovereignty in the celestial realms is acknowledged by Paul when he uses the title "Christ Jesus."
Charles H. Welch (1888-1967):
"The title of Christ Jesus seems to stress a new aspect of Christ's position and glory, pointing to the seated One at the right hand of God, rather than to the one who walked the earth and came only to Israel.
E.W. Bullinger (1837-1913):
Jesus was the name of his earthly life, and associated with him as the sin-bearer, The suffer, the man of sorrows. It was the name under which He was crucified. ....
"Jesus" was His earthly name, and suffering, sorrow and death were His earthly lot; but God raised him from the dead, and then all was changed.
God has made that same Jesus, whom you have crucified, both Lord and Christ. Acts 2:36
His official title. "Jesus Christ" Who came to His Own was set for the blessing of Israel, but Israel knew not the day of their gracious visitation....
In other books, therefore, we have this title 256 times, setting Him forth as a risen and glorified one, defining the believers position as justified and accepted in Him. Hence, believers are always said to be "in Christ," quickened with Him, raised with Him,sitting together in the heavenlies, with Him, blessed with all spiritual blessings in heavenly places in Him. We connect our position with him as Christ.
Charles Welch (1888-1967):
"The title seems to stress a new aspect of Christ position and glory, pointing to the One seated at the right hand of God, rather than to the one who walked the earth and came only to Israel ...
In all of this, course, it is always the same Person; only The title is changed. So, in the case of the title "Christ Jesus, "it is again the same person, but we do well to note that this particular title belongs exclusively to the ministry of the apostle Paul.
It is of design and with definite reference to the exclusive nature of the position indicated(The epistle to the) Ephesians speaks of those who belong to the church of the Mystery as being made to sit together in heavenly places "in Christ Jesus" (Ephesians 2:6) that when speaking of the high calling of God to the Philippians Paul adds "in Christ Jesus "(Philippians 3:14) or that when speaking of the holy calling those who were chosen before age-times, he should speak of that purpose and grace that were given to them "in Christ Jesus" (2 Timothy 1:8-9).
Simply put, "Jesus" Is the most usual name for the Lord during his earthly life, and is employed by the apostle Paul as the Resurrected Christ seated in heavenly realm. Both are associated with different dispensations, or Administrations.
Edited, To give an answer to the rest of the question.
"Is the usage "Jesus Christ" or "Christ Jesus" depends on the theological significance of Paul's using "through" or "in"?"
God reveals much through His usage of words. "Through" and "in" has great significance according to the connection through Jesus Christ and in Christ Jesus.
223. dia ►
dia: through, on account of, because of
1223 diá (a preposition) – properly, across (to the other side), back-and-forth to go all the way through, "successfully across" ("thoroughly"). ("thoroughly," literally, "successfully" across to the other side).
used as a function word to indicate movement into at one side or point and out at another and especially the opposite side of.
used as a function word to indicate passage from one end or boundary to another
: from the beginning to the end of.
Bearing that in mind what happened "through" Jesus Christ? So much that the world cannot contain enough books.
For the sake of brevity will sum it up.
He made the One not having known sin to be sin for us, so that in Him we might become the righteousness of God. 2 Corinthians 5:21
It was "through" the body of Jesus Christ that the world's sin was dealt with through the death, burial and resurrection.
It was complete. From the beginning of Jesus as a man, who tasted Adam's death , completed man's journey upward into the second Adam where He became a life giving spirit.
It made it possible to be put in Christ Jesus.
But you--and it is all God's doing--are in Christ Jesus: He has become for us a wisdom which is from God, consisting of righteousness and sanctification and deliverance;
1 Corinthians 1:30
The word "in" defined:
: that is located inside or within
1722 en (a preposition) – properly, in (inside, within); (figuratively) "in the realm (sphere) of," as in the condition (state) in which something operates from the inside (within).
"We were baptized into Jesus Christ into his death but were raised into Christ."
Created in Christ Jesus
Christ, is raising man into union with Himself, raises him into all that belongs to Him,into His divine life, and into partnership with His divine work--so that he dies in His death; rises in His Resurrection; ascends into His ascension; is seated with Him and His secession at the Father's right hand; and in His eternal life. A.J. Gordon (1836-1895)