AVB, you have not exhausted all the possibilities. The ones you mention may be the only ones conceivable to someone raised in a culture in which only words have real meaning and significance, and rituals must be verbally explained to be understood. Not all cultures and languages work that way. Some are actually closer to the opposite. I have heard it said that in Japan you are thought to be a very uncouth person if you have to come right out and say exactly what you mean, rather than taking the time and care to frame it in a metaphorical or non-verbal way. Of course, in America, we call it "passive-aggresive" to frame a message in a nonverbal or metaphorical way, rather than saying it directly.
I think this cultural difference is a big part of the reason many Americans would say it is "praying the sinner's prayer" or "giving testimony" that saves you, and baptism is just a picture of that. In other kinds of cultures, baptism saves you, and praying a verbal prayer or giving a verbal testimony is just the explanation for the uncouth.
Which is "real" and which is the illustration/explanation?