First, let me deal with your Jeremiah verse on Nebuchadnezzar... Yes, he is called a servant. The Hebrew definition in the case is manservant, bondsman or slave. That's a bit different from the Hebrew word for minister, which is (of all things) "minister". Now the Greek word for "minister" in Romans 13 has many meanings: attendant, waiter, a Christian teacher or pastor, a deacon or yes... a servant. The last one, and that's the one people want to use.
I have an expose for you. "Minister" appears in the Bible 161 times. 119 times it's used as a verb. Of the remaining 42 times that it is used as a title, there are only 6 times they refer to something other than a servant of God. Exodus 24:13 and Josh 1:1 are the first two. Joshua is referred to as the minister to Moses. 1 Kings 10:5 refers to Solomon's (the king) ministers. They were personal servants by the context given and not public servants. 2 Chr 9:4 is a repeat of 1 Kings 10:5. Gal 2:17 asks the rhetorical question of whether Jesus is the minister of sin. The last one I found is very interesting: 2 Cor 11:15 speaks of false prophets being ministers of Satan.
So there it is... 6 times where a minister is something other than a member of the clergy. That isn't a very strong supporting list, especially when nothing there pertains to a political structure.
"Ministers of God" or some variation thereof occurs 7 times in the Bible and EVERY TIME it speaks of the clergy.
With all this evidence, I have no problem saying that ROmans 13 is speaking about obeying the man of God.