Is "quintessential example" correct usage?
I would tend to think the word quintessential would not apply in this case as 'elementary particles' are a well-defined, factual and concrete concept.
When a class has certain, and usually multiple, subjective traits associated with it, then the best exemplar of those traits would be the quintessential member of that class.
If the class does not have a variable 'essence' then quintessential will not apply. Membership in the 'elementary particle' class is binary - either something is a member of the class or not. There is nothing variable about the essence of being an elementary particle.
You can say that the Higgs boson is the quintessential elusive particle that keeps modern physics interesting. Note that the words 'elusive', 'modern' and 'interesting' have added a subjective gradualism for which the search for the Higgs boson is the perfect exemplar.
Several dictionaries (eg, Collins, MacMillan, Cambridge) essentially agree with the definition of quintessential mentioned in the question. Thus quintessential example is effectively equal to most exemplary example, which from a pedantic point of view is a bit redundant. However, aside from those pedants who recoil in horror from quintessential example as a monstrosity, most English speakers will have no trouble understanding what is meant.
As suggested in akberc's answer, it is slightly perverse to refer to the electron as the quintessential apparently-elementary particle, when most of the 31 elementary particles are representative only of themselves, rather than being representative of elementary particles in general. But that is a semantic-content issue, rather than an English-language question. From a language point of view, your alternative wording is better than the first. However, the parentheses around apparently are a noisome distraction and should be dropped. Or in some other sentence explain that wherever you write elementary you actually mean apparently-elementary, or elementary according to theory X, etc.