All of the original United Baptist articles of faith that I can find contain total depravity and election by grace. Do any of them still preach this doctrine or have they
all moved over to general atonement?
Brother, your question is a fair one, and the answer is that they have not all moved, though the question may rest on a false choice.
The United Baptists were never built on a choice between election and general atonement. When the Regular and Separate Baptists came together in 1801, the Terms of General Union were written so that brethren who held to particular election and brethren who preached that Christ tasted death for every man could sit at the same table. Neither side was asked to surrender the doctrine it loved. The Union only asked that the difference not break fellowship.
So you will find the old articles still standing in most of our churches: man fallen and unable to save himself, and salvation by free and sovereign grace. You will also find that many of our preachers press the gospel upon every sinner without apology, and rightly so. "Whosoever will, let him take of the water of life freely" (Revelation 22:17) is as much the Word of God as "As many as were ordained to eternal life believed" (Acts 13:48).
My own conviction is that these two are not enemies. Christ's death is sufficient for all and offered to all, and God's special purpose in it is the saving of His own. I do not make election a reason to hold back the invitation, and I do not make the invitation a reason to deny that salvation is of grace from first to last. It is not that we have moved off the old doctrine. Some have simply stopped saying the half they find hard, and others the half that is plain.
As to whether any still preach it, yes, and the faithful ones preach both together.