You have asked an excellent question relevant to both the Language and Usage parts of ELU. From a language point of view, this construct is called (as you note) the adjunct noun, which labels a noun that acts as a noun modifier. From a usage point of view, you ask what rules govern its employment. This is mostly a matter of style, which is to say that opinions will differ and answers won't come as simple rules like "make your subjects agree with their verbs."
First of all, you'll simply have to learn the adjunct pairs that have made it into the language as a unit. For instance, brick wall. There are few occasions when you'd use "wall of brick." One clue is that the digram has become idiomatic:
I've never met someone so stubborn. Arguing with him is like talking
to a brick wall.
Sometimes you can spot digrams on their way to union. For instance, we once had head phones and headphones, but sometime around 1925 according to the Ngram viewer, the latter took off and left the former to disappear. Sometimes these usages go through a hyphenated stage. Recently someone asked here about which of touch screen, touch-screen, and touchscreen to use as he'd seen all three. I don't know which will win, but in these cases I'd stick with the adjunct usage.
Next, be careful to watch for situations in which the adjunct noun phrasing differs in meaning from the transposed prepositional phrase. For instance, consider the following two sentences:
The usual value of the density of water is one gram per cubic
In the ocean, the water density increases with
The first phrasing is about a physical constant; the second, about a measured parameter. They're not interchangeable.
Avoid ambiguity. What does the following mean?
A Victorian glass house
Is this a house made of Victorian-era glass or is this a Victorian-style house made of glass? Or is it both, like the Crystal Palace?
I think you're right that things get worse with more adjuncts (more of which later), but in your example, Cimenterie Nationale d'Haïti is a proper name and is only one adjunct. As far as I can tell, the closer the proper name is associated with products, locations, etc., the more likely the adjunct is favored, so for General Motors, we'd say
a GM car, a GM plant, the GM board of directors
but not "a car of GM." That usage is fine for
the bailout of GM, the history of GM, the control of GM
Speaking of proper names, use the locution favored by the owner. In California there's a town called "City of Industry." It's never called "Industry City." You'd think it would be easy to tell, but is it "New York City" or "The City of New York"? I once looked it up, and official documents use both interchangeably, so I guess all of us can.
Stick with the adjunct when it's a useful shorthand for a complicated explanation. For instance safety glass is glass that's designed and manufactured to be less likely to break than ordinary glass and to be less dangerous than ordinary glass when it does break. There's no good alternative.
The inverse are those adjuncts for which we already have perfectly good terms. Is there any reason to say
John has an alcohol problem
John is an alcoholic?
I'd avoid adjuncts combined with possessives.
The family summer house
is probably fine, but I'd prefer
The selling price of the family summer house
The family summer house's selling price
As you noted, piling up adjuncts is problematical:
The Budget Committee
The State Budget
The Illinois State Budget Committee
State Budget Committee Evaluation
The Illinois State Budget
Committee Evaluation Report
The Illinois State Budget Committee
Evaluation Report scandal
The longer the list, the more your readers have to keep in memory before they get to the object of discussion. Where to stop? I'm afraid there's no hard and fast rule.
When adjuncts are nominalizations of verbs, they can undermine the force of the associated verb:
supporting child soldier recruitment suppression
suppressing the recruiting of child soldiers?
I'm sure that skillful writers can add more consideration, and indeed I'm sure some will disagree with my observations.
A final thing: in "table of contents" I'm used to calling contents the object of the preposition, but others call it a prepositional complement.