Bab, personally, I view the phrase "rightly dividing the word of truth" as a reference to laying out aright one's truth based word to others, as that is what Paul is relating to Timothy as to Paul's desire that Timothy put his audience "in remembrance" of "things."
At the same time, Paul communicates his point to Timothy, there, in 2 Timothy 2, by way of a CONTRAST TO, or DISTINCTION TO that - BOTH by his use of the word BUT - in the very next, CONTRASTING passage, BUT ALSO by way of his relating to Timothy the ERROR CONCERNING THE TRUTH of two individuals he mentions there, who had apparantly failed as to WHERE as to A TIME LINE of some sort they had placed "the resurrection" obviously YET FUTURE from Paul and Timothy, as PAST ALREADY."
In other words, Paul, could not but have to DIVIDE BETWEEN those issues PRIOR TO AS WELL AS THIS SIDE OF the Mystery revealed to and through him by Christ, Col. 1:23-29.
The brother was constantly using phrasing like BUT NOW, etc., as had Christ, given the DISTINCTION between "the Law and the Prophets" and His own "BUT I say unto you.." as a transition was "at hand" then too.
As for our constant emphasis of Paul's ministry, consider that Christ had consistently emphasized Moses - "what did Moses say... write... command." Its that same kind of emphasis as Paul is to the Body what Moses is to Israel.
Regarding kingdom of heaven/ of God phrasing, I see them as interchangeable terms, at the same time that I recognize their DISTINCTION in meaning as to the will of God ON EARTH in CONTRAST TO His will IN HEAVEN.
Lastly, we see the Body as comprised of both Jew and Gentile as fellow-heirs WITH Christ over His HEAVENLY realm - the will of Heaven IN Heaven.
We see those Jews saved into the Body as having begun AFTER Israel was concluded UNcircumcision, their only salvation then/now through Paul's Christ given "my gospel... OF the UNcircumcision" that both said Jews and Gentiles THIS SIDE of disobedient and gainsaying Israel now had to avail itself of.
We make a DISTINCTION BETWEEN that AND the election of Israel - they of the circumcision which had believed BEFORE disobedient Israel was cut off from THEIR "gospel OF the Circumcision," AT THE SAME TIME that God sealed that election of that nation unto another day - that day of "how much more their fullness."
So, yes, but we mean God's TWO-FOLD Purpose - His Prophesied Purpose as to the election of that nation as His Royal Priesthood over the nations of this EARTH one day, Isaiah 2:1-5; 61: 1-6 and His Kept Secret Purpose as to A New Creature: the Body of Christ; His co-heirs with Him, as His fullness of Him that filleth all in all those Heavenly Places, Eph. 1:3; 19-23.
Its the finer DISTINCTIONS in these things that have you scratching your head
"For this cause I bow my knees unto the Father of our Lord Jesus Christ, Of whom the WHOLE family IN Heaven AND Earth is named," Eph. 3: 14, 15.