IMO, the main decision points are I) Meaning and II) Modifier
Modifiers usually go hand in hand with Logical Meaning, so one should rely on grammatical rules, but rather understand the intended meaning. Wrong placement of Modifiers change the meaning. Why in fact does a wrongly placed modifier change meaning? It is important to understand the function of modifiers. Modifier give a description of an object! So if you misplace the modifier you describe something else than is actually true. So to go through the ACs.
A) -ed Partial modifier clearly modifies Edith Sampson. There is no other entity that could be modified. The passive voice clearly describes who appointed the position. Meaning: Harry Truman appointed Edith to the position. She became the first African American women to be named an official representative....
B) Prepositional Phrase IN Edit Sampson is not logical. Also meaning has changed: Harry Truman appointed the first African American women
to be named an official representative.
C) Harry S. Truman appointed Edith Sampson to the position as the first AA woman -> Clearly not the intended meaning: He appointed her to the position, but not as the first AA woman... that she became the First AA woman was the result!
D) The first AA women is a noun modifier, therefore must touch E -> This indicates that Harry Truman is the first AA woman...
E) Appointed as the first AA women to be named? -> Clearly not intended meaning: She was appointed to a position that made her then to the first AA woman...