The answer is that the basic premise of the question that there are four discrete children, and all the Midrashim refer to "the same child", is baseless.
In reality, the pashut peshat is that the four verses are synonymous. Pashtanically, for example, "what is this service to you" is not an antagonistic mockery, and it is not interpreted this way by any of the non-Midrashists, e.g. Ibn Ezra and Rashbam. Similarly, none of the other 3 verses describing the questions of the sons are interpreted by these Rishonim as referring to discrete unique questions. (Although admittedly, they are fairly bland questions anyway; it is this verse that most starkly demonstrates the difference between the peshat and the derash).
Accordingly, the starting point is simply four seemingly equivalent verses about relating the Exodus to one's children, which are then Midrashically developed into discrete answers for discrete children. It is the Midrashim themselves which develop these verses into children; not as the question implies "so many different ways to refer to the same child" that the profiles were preexisting.
Regarding the distinction between tam and tipesh, it should be noted that this is not necessarily even a Midrashic dispute; let alone one bordering on Peshat. The Midrash Sekhel Tov (Exodus 13:14) for example explicitly equates 'tam' and 'tipesh':
מה זאת. זו מדת תם, דהיינו בן טפש שאינו מבין מדעתו ולא למד מאחרים ואינו רשע וכופר, אלא בתמותו שואל מה זאת העבדה
That is, it appears that the terms are simply synonymous in context.