My choice is
(D). It took me 1 minute and 39 seconds.
(A) The basic structure of the modifier at the beginning of the sentence is: With an elaborate menu featuring dishes as well as X. We can interpret as well as X in two ways:
(1) as well as X is parallel with "featuring dishes". Both X and "featuring dishes" modify "an elaborate menu". But, it does not make sense to write that "a menu serves its signature breakfast fare". So, we have to find an alternative reading.
(2) as well as X is parallel with "an elaborate menu". In this case, X should be a simple noun for parallelism.
A is incorrect because either interpretation does not make sense.
(B) Here, the 2nd interpretation works. "An eatery established downtown" means differently from "an established downtown eatery", which is used in the original version. I, however, do not believe that original version must convey the intended meaning. My reason to rule (B) out is that "An eatery established downtown" can be simplified to be "A downtown eatery". Adding established here is superfluous and even pretentious (after all, an eatery feels like a rather humble place. But, on that, "elaborate menu featuring innovative dishes ..." is just as unnecessarily florid.)
(C) It makes it clear that "with serving its breakfast fare" is supposed to be parallel with "with an elaborate menu". In that case, they are not parallel.
(D) More... than. That is good.
(E) The difference between (D) and (E) lies in the predicates. In (E), the only issue I have about "offers more of a diverse selection of food as any other restaurant" is that I expect to see either "more ... than" or "as ... as / not so ... as". But I only see "more ... as".