But I (and I do not think I am unique in this) have pondered long and hard and have emerged intellectually persuaded of the Baptist position, though I am not from a Baptist family or background, nor was I brought to faith in a Baptist context.
What is the "Baptist position"?
That those who accept Christ and have been born again and who accept the essential doctrines (e.g. the Trinity) of Christianity are part of the invisible Church and that it is not necessary to have visible unity or agree on the non-essentials to be part of the invisible Church.
Hmmm... I think you are mingling different themes. I assumed the thread is only about ecclesiology, but your reply seems wider, reaching out into soteriology, and what doctrines might be deemed particularly characteristic of Evangelicalism. Forgive me if I have misunderstood you.
In re the church, we hold that each congregation is autonomous, that is, runs its own affairs subject to the Headship of Christ. Thus we have no wider authority, such as bishops. This is not the same as isolationist, as we believe in voluntary association, fellowship and cooperation between local churches. But no external authority wields power over the local church. This, of course, is not uniquely Baptist, as it is held also by Congregational churches, by (I believe) the Assemblies of God, and many unaffiliated independent congregations. Membership of a local church is through baptism, which of course means of believers: but I do not think that is unique to us either. So a church is a body of baptised believers who meet regularly for fellowship, prayer, teaching, and the Lord's Supper.
Yes, we hold "the essential doctrines of Christianity" such as the Nicene Creed, though we give a different interpretation to the Greek pronoun 'eis' regarding baptism 'for' the remission of sins: more like a wedding ring, which does not efect the marriage, but is an important element for it.
What characterises Evangelicals (among which we are) is usually agreed to be four matters: a strong view of the authority of scripture; an active, expansionist commitment to evangelism; the centrality of the Cross; the need for the new birth which takes place when a person believes and is justified before God. I would add the doctrine of assurance: the witness of the Spirit that one is a child of God.