Many manufacturing majors have notched up more sales growth than

If you consider the meaning "Far in excess of" is used to compare two or more things which is the base of the statement. While using "far exceeding" means its already in extra. But from what? Far exceeding is making statement ambiguous that's why "far in Excess of" is the better words choice.

Hi there,
I would see this from a meaning perspective. Underlined portion signals that the question is indeed about comparison. So what are being compared here?
Manufacturer's sales growth, their previous achievement and the achievement of the fastest growing new economy companies.

A. fastest should be preceded by 'the'. So Eliminate.
B. far exceeding makes the sentence a fragment. i.e, Manufacturing majors have did X, and far exceeding Y ... Ideally, far exceeding makes the sentence parallel with the main clause. So this should be followed by a complete sentence. Something like, Far exceeding other's growth, Majors boasted their growth would have been a fit there. But since the sentence stops at far exceeding Y, the entire sentence becomes fragment.
C. Fastest should be present, because, the word 'even' warrants for the superlative usage. If you want to be conservative, hold on to this.
D. Same as B. So Eliminate.
E. far in excess of that of even the fastest growing new economy companies.

Now compare C and E, what do they make? they make the phrase parallel to the comparison of sales growth. More sales growth than X and Y.
Here X is their previous sales growth, and Y is the sales growth of even the fastest growing companies. Now the sentence is parallel and makes sense. Eliminate option C for incorrect superlative usage.

Answer is E.

Hope this helps.

Explanation for choosing between exceeding and far in excess:

Meaning based understanding: The verb-ing modifier after or before the comma can modify the noun or the verb of the core clause, but in each case the doer of the verb-ing modifier is intended to be the subject of the main clause.

Exceeding, as used in original sentence can represent a result but the subject 'manufacturing majors' can not be the doer of the the effect exceeding. Imagine saying Many companies exceeding the growth of other companies vs Growth of many companies exceeding the growth of other companies.

So in this fact lies the clue that for exceeding the subject of the core clause can not be the "doer" in this case. So clearly we will not be using "exceeding here".

Now choosing between C and E, comparison is clearly to be established between a bunch of companies which are believed to be the fastest and the subject companies, many manufacturing majors, majors with notched up sales.

Option E survives.