We have those. For us, the office in question in Titus 1, 1 Tim 3:1-7, and Acts 20 is the same office with three aspects: episkopos, presbeuteros, and poimen -- bishop, elder, shepherd. Acts 20 and 1 Peter 5:1-2 show all three aspects referring to the same office. We believe this office is only over a local, autonomous congregation with the only central authority being Christ.Yes, Paul is telling Timothy to transmit the teaching he has given to him, but he also is saying that this teaching should be committed to faithful men. Both the teaching and the men are important. It is clear from Titus 1:5 that Paul wanted Titus to ordain other men as presbyter.
I enjoy your insight.
The bishop/overseer aspect is about authority over the congregation which they have to deal with discipline and make executive decisions necessary for the ordered operation of the congregation. Elder/presbyter is the wisdom of an experienced guide (which is why Mormon "elders" are somewhat amusing), and the shepherd is about feeding them spiritual food necessary for growth and protecting them from outsiders meaning to do them harm (e.g. false teachers). The authority of the elders does not extend outside of scriptures, they must meet all qualifications given in Titus and Timothy, and there must be a plurality who are equal in their authority over each congregation. We believe this is the Biblical pattern to the extent that even some of the Apostles also held the office of Elder (Acts 15; 1 Peter 5).
Again, I'm not analyzing your faith, I'm just explaining how the church of Christ understands things. I don't believe anything I've said is outside the authority of scriptures so far.
P.S. My dad was an elder of our congregation for almost 20 years.