The word "synecdochic" exists and you can use it in this context, but it's a matter of lightning and lightning bug. Isn't the word "emblematic" more appropriate? We're not just using a part to signify the whole; we're stating that the part typifies the whole, and "emblematic" embodies both of those meanings. Besides, it's less likely to confuse, and applying Occam's razor to language, the best word is the simplest one that most closely approximates the intended meaning.