So where does a conservative secular atheist fit into this paradigm?
That's for that person to decide. I would only say that the Declaration of Independence is this nation's birth certificate." It identifies our entire reason for being, our purpose, our identity. If you don't believe in the "laws of nature or nature's God," you have to resolve and reconcile the source of this nation's very right to exist. Obviously you would be at odds with our founders who found their (and by extension, "our") right to exist in some absolute source that existed on a level higher than any man or concensus of men.
That person would further have to resolve that somehow we are endowed with certain unalienable rights, and yet, there is no party that does the "endowing."