I'm not sure what you mean by "a modifier starting with a singular noun".
So I don't understand the question ("is it possible for a modifier starting with a singular noun to refer to another plural noun?")
Your first example is wrong because of meaning rather than grammar: simply because Pavlov's Grenadiers is not a soldier.
Pavlov's Grenadiers does consist of soldiers, so the second example is PROBABLY acceptable.
(I'm uncomfortable because "Pavlov's Grenadiers" is a name and probably singular, while "soldiers" is plural.)
MartyTargetTestPrep's version is the best, because Pavlov's Grenadiers IS a regiment.
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