Sentence Correction

A recent poll indicates that many people in the United States hold a combination of conservative and liberal political views; i.e., they denounce big government, saying government is doing too much and has become too powerful, while at the same time supporting many specific government programs for health care, education, and the environment.

(A) they denounce the big government, saying government is doing too much and has become too powerful, while at the same time supporting

(B) they denounce big government- they say that government is doing too much and has become too powerful-but supporting at the same time

(C) they denounce big government, say that government is doing too much and it has become too powerful, while they support at the same time

(D) while they denounce big government, saying that government is doing too much and has become too powerful, at the same time supporting

(E) while they are denouncing big government- they say that government is doing too much and it has become too powerful-supporting at the same time

IMO A
You can proceed by POE

conjunction BUT is used to show contrast but it is used to connect to independent clauses. "supporting at the same time" is not a independent clause ------> Eliminate

[C] is kind of incomplete or run-on like sentence. "they denounce big government, say that government" can be either "they denounce big government and they say that government" or "they denounce big government, saying government"

[D] & [E] doesn't look good to me. I am not sure reason of eliminating the options but what I thought was
Placing while at the start to show contrast can be used but after comma the part "at the same time" doesn't fit without while.
I also want to know other the grammatical flaws, if any, in both [D] & [E]