Sentences with many dependent clauses

Grammatically, there's nothing wrong with nesting subordinate clauses to any number of levels. Here's a sentence from a well-known children's song, "This Is the House That Jack Built":

This is the rooster that crowed in the morn
That woke the judge all shaven and shorn
That married the man all tattered and torn
That kissed the maiden all forlorn
That milked the cow with the crumpled horn
That tossed the dog that worried the cat
That killed the rat that ate the malt
That lay in the house that Jack built.

Legal writing often contains long sentences with very complex structure. Here is just part of a long sentence from a compact between two U.S. state governments:

Whereas, The primary purposes of the project by which said lake was created was to conserve water draining said swamp, all of which has its source in Pennsylvania, as well as control floods and regulate the flow of water in the Shenango and Beaver rivers, and secondary thereto, permit the water and the land surrounding the same to be used for fishing, hunting, recreation and park purposes, under such terms and conditions as the water and power resources board might determine, in such way or ways as in the opinion of the said board will not materially interfere with the primary purpose in said acts of assembly and hereinbefore specifically referred to, and …

Long, complex sentences are also used in ceremonial speeches, commemorative plaques, or short biographies that summarize a person's life in one paragraph. In those places, there is a need to pack a lot into one sentence. For example, here is the text of one commemorative plaque:

Dedicated to the memory of the American Merchant Mariners and the U.S. Navy Armed Guard who gallantly went down to the sea in ships while defending the freedom of the United States of America during the time of war.

Your example sentence sounds like it might be part of a short biography of John McCoy or maybe a plaque placed on the monument or maybe a short encyclopedia article about the monument.

Thus a very long, complex sentence can establish a certain tone—playful, legal, ceremonial, or summary—which may or may not suit the situation where you're saying or writing it. But such sentences are certainly grammatical.

Clarity and emphasis

It requires some skill to keep a long sentence clear. Skillful use of subject-verb agreement can help a reader or listener follow the sentence without confusion—but the writer can easily become confused and make a mistake. The second "was" in the sentence from a legal document above doesn't agree with "purposes"—a genuine grammatical error. The author got confused by the upcoming "as well as" and whether the following "to" governed just "conserve" or also "control", "regulate", and "permit". It would be useful here to repeat "to" before each verb.

Another pitfall is that pronouns can become unclear if there are too many reasonable choices for antecedents. For example:

The world-renowned monument-maker John McCoy, the son of an Irish immigrant from County Kerry, home of Carrauntoohil, Ireland's highest peak, whose first visit to Shelbyville left a permanent mark on every tavern in the city, began his career making signs along mountain roads.

It's not clear whether whose refers to John McCoy or his father.

Your example sentence seems pretty clear, though I wonder if the last "his" was intended to refer to John McCoy or his father.

Regarding the choice of whether to break the sentence into smaller sentences, this is a stylistic choice, depending on the kind of tone you want to set and which facts you want to emphasize. Your example sentence emphasizes the fact that John McCoy built the monument most of all; the other facts sound like background information, of secondary or minor importance. If you wanted to emphasize the fact that McCoy and his father both lived near Brooklyn, you could write it like this:

In the 1980s, John McCoy was president of *** company. During this time, he lived in the vicinity of Brooklyn—the same place where his father had settled and started his own first career.

Very often, the best solution to a problem with how to include some information in a sentence without wordiness or awkwardness or lack of clarity is not to resequence it, regroup it into smaller sentences, or rewrite it at all, but to delete it. If the secondary information is causing annoyance and isn't important anyway, just omit it:

This monument was erected by John McCoy, the famous Brooklynite and entrepreneur.

Really, your sentence doesn't seem especially long to me, nor does its structure with several dependent clauses seem remarkable. Compared to the first two sentences above, your example sentence is negligibly short. It's not even as long as my own made-up sentence about John McCoy, which isn't all that long. If it has a problem, it's that the emphasis isn't clear. If the point is that John McCoy erected the monument, what's the relevance of the other information? However, context might make that clear.