Your interesting question pertains to sociolinguistics. Human language is a symbolic system that adapts and changes as needs adapt and change. Many human needs are ideational as well as practical needs. For instance a military chief needs N men, and rather than taking forever to describe what sort of men he calls them "rifles" or "pikes" and so forth. Another example of synecdoche shows how it expresses feelings: Lady Macbeth "Take my woman's milk for gall----".Then there is "all hands on deck!"
Synecdoches not only save time and effort in practical ways , they also express feelings by honing in on a part of the whole that arouses feelings as a matter of tradition or even perhaps as selecting detail that has a priori significance, for instance fear and loathing are felt in the belly so I have no belly for killing.
What do synecdoches receive? From where or whom or what, do synecdoches receive?
Not all parts represent the whole in our minds. My toenail does not represent my forum persona but my brainmind does. Quiet there in the back row!
Synecdoches like all metaphors and symbols are understood intersubjectively(culturally) except for those that apply to a body part that actually feels a feeling or emotion.
Synecdoches are inseparable from the psychosocial and are therefor not amenable to formal analysis. I think your etymological analysis has gone as far as it can go. I'd like to know if you yourself can formally analyse synecdoches further than you already have via etymology.
Synecdoches involve outwardness like any concept involves outwardness or else it could not be conceptualised. This world is a relative world.
Synecdoches are inert, do not receive until they are used by living people as part of other, living language. When synecdoches are over- used in living language they become cliches.