Something to add.
Pilgrim, I thought I would add something to the discussion that I believe explains the Reformed Baptism a little more. You probably already know most of it already; but I thought it might be useful to the conversation.

I believe it is very important to emphasize the difference between two different groups that believe in ‘Believers Baptism’.
Dispensationalist, Mennonites do not appreciate God’s fundamental unity of the Bible and God’s covenant dealings with His people. Therefore they reject paedo-Baptist arguments from the covenants and regard the New Testament data as by itself conclusive for believer’s baptism. In other words they say that was just Old Testament teaching, this is the New Testament.
That group gets the scorn of the Reformed paedo-Baptist community and rightfully so.
Reformed Baptists on the other hand like their Reformed paedo-Baptist brothers and sisters recognize that the Old Testament is still relevant. However, believe that it supports their positions, not the Reformed paedo-Baptist position. There is a certain parallel between Old Testament circumcision and baptism (Romans 4:11; Col. 2:11-12). Both were rites or symbols induction into the covenant people of God. For more, I recommend ‘A Modern Exposition 1689 Baptist Confession of Faith by Samuel Waldron.

Tom