The outspoken abolitionist senator Charles Sumner, after delivering a

First of all the appositive and absolute phrase are completely different things. The one in option E is an absolute phrase, not an appositive. The difference is as follows:

An appositive is a noun or a noun phrase modifying another noun:
John, the most brilliant student in the class, could not solve this problem.
Tabby, my cat, is ill.

An absolute phrase on the other hand has the structure noun+noun modifier, and it modifies the complete clause (not any particular noun) in some way:

Here, "an action (that) Brooks carried out with impunity..." is an absolute phrase (noun= an action, noun modifier (that) Brooks carried out..."), and this absolute phrase modifies the whole clause "who bludgeoned the senator".

Coming to your example: "a position" is an appositive modifier for "account manager", but this appositive is again modified a relative clause ( modifier of modifier - appositive modifiers are nouns themselves). Thus the example that you gave and the option E use different types of modifiers.