Bob,
In all fairness I no longer consider myself a part of the SBC. The SBC used to be a much larger tent than it is now, and I am willing to concede that the fundamentalists now control the organization and its machinery.
Since there have been so many streams in the baptist tradition, it's hard to answer your question, but I'll try my best with each of the areas you mentioned:
Polity - Without question I think the conservatives (whom the fundamentalists call "moderates" - you see the difficulty with those labels) and the liberals have a leg up on the fundamentalists here. The fundamentalists have essentially turned a formerly bottom-up, cooperative missionary organization (the SBC) into a tool for theological orthodoxy. They have also abandoned traditional baptist views on priesthood of the believer and the separation of church and state.
Ideologies - Well, if we limit it to Southern Baptists, we have to recognize that the fundamentalists and the liberals are a long way from their forbears. For instance, despite some revisionist history to the contrary, the SBC clearly grew out of Southern Baptists desire to protect the institution of slavery. In addition, temperance/prohibition did not become an issue until the late 18th century.
There was conflict among baptists regarding women in ministry as far back as Anne Hutchinson, so this is also a confusing area for the "historical" baptist.
Certainly my views on homosexuality would have put me in the minority among our baptist ancestors, but I (along with many of my colleagues) am actually more conservative on issues of congregational accountability and the role of the church in the community than many fundamentalists.
Still, I would conced that ideologically, in some areas, I am farther from many of our baptist forbears than most fundamentalists. Nevertheless, polity and piety (not ideology) have traditionally (until the fundamentalist takeover) defined baptists, so I think this is the least important of the four issues for determining our baptistness.
Theology - Here you might need to distinguish between the urban, liturgical (Charleston) tradition and the rural, informal (Sandy Creek) tradition. Charleston tradition clergy are traditionally seminary-educated people whose theology is consistent with that of the mainstream Christian community. That is still the case among conservatives and liberals, who primarily come from that tradition.
On core issues: divinity of Christ, sinfulness of humanity, bodily resurrection, significance of the ordinances, etc. I think we are all in agreement and likewise with our forbears. On issues of scholarship and biblical interpretation, I think we are as faithful to our tradition as the fundamentalists are to theirs.
Practice - Again it is wise to distinguish between the Charleston and Sandy Creek traditions. The liturgical worship and ecumenism in our church is consistent with the baptist churches of our tradition.
Joshua