Very informational post by e-GMAT!
I almost took a little over 2 minutes (30 seconds to choose between C and E) and arrived at E only due to parallelism.
C is in active voice and E is in the same voice as the clause before the underlined part.
Is is safe to assume that this is a 700+ question? I have hardly observed such ellipsis at play questions on the mocks that I have given

Like many SC Q's this is a direct pick up from NY Times

http://query.nytimes.com/gst/fullpage.h ... A965958260

E is correct.

As goalsnr said, So X, So Y that Z is perfectly correct. Other wise NY Times would not use it.

So dogged were her investigations of the garment industry, and so persistent her lobbying for wage and hour reform, that she was first recruited by Gov. Al Smith, and later by Gov. Franklin D. Roosevelt, to work within New York State government, rather than against it.

RonPurewal wrote:

If it's a correct answer, it's a correct answer.

This is a really, really old problem (over 10 years old, if it's in "set 27"). The current GMAT won't test such oddly constructed sentences, so it's best to forget about this one altogether.

why the second clause contain no verb
I think
so persistent was
is better.

very strange pattern

The NYT statement is as follows:
So dogged were her investigations of the garment industry, and so persistent her lobbying for wage and hour reform, that she was first recruited by Gov. Al Smith, and later by Gov. Franklin D. Roosevelt, to work within New York State government, rather than against it.

"and" is missing in option E. How can it be correct?

mikemcgarry, please help...

So dogged were Frances Perkins’ investigations of the garment industry, and her lobbying for wage and hour reform was persistent, Alfred E. Smith and Franklin D. Roosevelt recruited Perkins to work within the government, rather than as a social worker.

A. and her lobbying for wage and hour reform was persistent, --> Wrong Structure: So X , and Y (missing "That")
B. and lobbying for wage and hour reform was persistent, so that --> Wrong Structure: So X , and Y, so that Z
C. her lobbying for wage and hour reform persistent, that --> Structure is correct "So X, Y, that" but Y does not logically fit into sentence, also X and Y are not parallel
"So dogged were Frances Perkins’ investigations of the garment industry, her lobbying for wage and hour reform persistent, that"
D. lobbying for wage and hour reform was so persistent, --> "that" missing
E. so persistent her lobbying for wage and hour reform, that --> Correct structure: So X, so Y, that Z

Since the questions are pertaining to the structure of the correct choice, I will only take that one in my response.

So dogged were Frances Perkins’ investigations of the garment industry, so persistent her lobbying for wage and hour reform, that Alfred E. Smith and Franklin D. Roosevelt recruited Perkins to work within the government, rather than as a social worker.

I will simplify this sentence for my analysis:

So dogged were FP's investigations, so persistent her lobbying for wage and hour reform, that AES and FDR recruited Perkins to work within the government.

There are certain specific things about the structure of this sentence.

1: Inverted Structure

If this sentence were written in a more straightforward way, it would be as follows:
FP's investigations of the garment industry were so dogged that AES and FDR recruited Perkins to work within the government.
(notice that I have not considered the second element in this sentence for the sake of explanation. I will consider that in my analysis below:) )
Now to come up with the sentence in question, simply flip the order of the SV in the first clause in the simple sentence above. This will get us to the following version:
So dogged were FP's investigations, that AES and FDR recruited Perkins to work within the government.

2: Idiom used

Let's take the simplified version of the sentence (I will show both inverted and straight sentences)
- FP's investigations of the garment industry were so dogged that AES and FDR recruited Perkins to work within the government.
- So dogged were FP's investigations, that AES and FDR recruited Perkins to work within the government.
So as you can see, the idiom that has been used here is "So x that Y".

3: Two entities connected using a comma

I understand that there are two elements in the list but they have been connected using a comma. Let's consider the straight version of this sentence:
- FP's investigations of the garment industry were so dogged AND her lobbying for wage and hour reform was so persistent that AES and FDR recruited Perkins to work within the government.
In this version I would have added the second element using an AND.

Now let's consider the inverted structure.
- So dogged were FP's investigations AND so persistent was her lobbying for wage and hour reform that AES and FDR recruited Perkins to work within the government.
Here also I would have added the second element using an AND

So why is there is no AND and a COMMA instead - I do not know. I can almost say that it is a style of writing and certainly not a common style of writing.

4: Ellipsis

As you can see, the second element does not contain a verb. In fact ellipsis is at play here. Here is another sentence with similar ellipsis at play:

Of all the wild animals in their area, none was more useful to the Delaware tribes than the Virginia white- tailed deer: it was a source of meat, and its hide was used for clothing, its antlers and bones were used for tools, and its sinews and gut were used for bindings and glue.

Notice the verb "was used" in the first element.
Notice no verb in the second and third elements. But here ellipsis is at play.

Take away

- Follow the process for solving the question. Eliminate choices on deterministic errors and then consider errors such as punctuation etc. Yes, while you are preparing for GMAT, you must understand the construction of the correct sentence, but when you are in test environment, be confident of your approach and do not second guess yourself if questions such as these appear.

I hope this helps.

Regards,
Payal