“Those words fit the Greek quite well.”
Not really. The word translated “church” simply means gathering. It is used in the NT for a riot. No connotation of a top-down church.
Same for “bishop”. It means elder or overseer, which is why modern translations use those words - except the NKJV. They want to echo the KJV.
There is no basis for believing Paul envisioned a medieval “bishop”. King James wanted to translate things “High Church” because, without a hierarchical church, his divine right to rule would come into question.
The word ekklesia does NOT refer to a riot, to an irregular one-time lawless mob adventitiously gathering. In Acts 19 the local Ephesian silversmiths had been summoned (called out) by one of their prominent artisans, albeit unauthorixed to do so, but it was for a purpose: to consider an imminent threat to their means of living. However, without a ruling elder, it degenerated into a riotous uncontrolled mob scene. Upon the arrival of the second-highest government official the crowd became stilled and came to order, whence the official took control. He referred personal issues to the courts, and that discussion of guild issues to an assembly of lawfully summoned parties.
The wod ekklesia translated "church" in 1611 was entirely appropriate, where ekklesia is an adjectivial use of the participle of the verb "to call out by summons" to describe the group identified as "The Called-Out (Ones)" or "Summoned Ones" who in the Christian culture represent the local constituents of the group that is by mutual agreement summoned to congregate for worship iin the breaking of bread, prayer, instruction in the doctrine of the Apostles, and/or dealing with practical communal affairs. The regularly established meetings/gatherings of the church members are usually moderated by mature reliable spiritual elders, one of whom may be the ruling episcopos/bishop/bearer of the Sword of the Spirit, which is the Word of God, rightfully asseverated for the application of doctrine, for reproval ofimmature behavior, for correction of errors arising from misapplication of or disobedience to the Word, and for practical training of congregants in progressive holiness.
According to Marvin Vinent in his "Word Studies":
The office of a bishop (ἐπισκοπῆς)I believe your treatment is colored by your desire to set aside the difference between the task of translation versus the burden of finding meaning to the translation, which is the interpretation of it, succeeded by the practical exercise of applying it. Whatever uninspired and fallible humans have done bu creating a supra-church episcopacy, and wedding that external demonic structure to the state thus contaminating the terms "church" and "bishop"--that is noy a translational error, it is a method o using the terms in a sort of double-speak undermining of the New Testament use of thm.
Ἑπίσκοπος superintendent, overseer, by Paul only in Phi_1:1. The fundamental idea of the sword is overseeing. The term ἐπίσκοπος was not furnished by the gospel tradition: it did not come from the Jewish synagogue, and it does not appear in Paul's lists of those whom God has set in the church (1Co_12:28; Eph_4:11). Its adoption came about in a natural way. Just as senatus, γερουσία and πρεσβύτερος passed into official designations through the natural association of authority with age, so ἐπίσκοπος would be, almost inevitably, the designation of a superintendent. This process of natural selection was probably aided by the familiar use of the title In the clubs and guilds to designate functions analogous to those of the ecclesiastical administrator. The title can hardly be traced to the O.T. There are but two passages in lxx where the word has any connection with religious worship, Num_4:16; 2Ki_11:18. It is applied to God (Job_20:29), and in N.T. to Christ (1Pe_2:25). It is used of officers in the army and of overseers of workmen. The prevailing O.T. sense of ἐπισκοπὴ is visitation for punishment, inquisition, or numbering.