Is this the correct use of the word synecdoche: "Beer, brats, and cheese are pretty much synecdoche of the entire state of Wisconsin."?

A synecdoche is a literary device where a word or concept is indicated by the use of another word (the synecdoche) that is a part of the first one. For example, I can say:

Boston won by 6

where Boston refers to the Boston Red Sox (that city's baseball team) and 6 refers to 6 runs - the winning margin.

Now to the question.

• If we were to try to make a synecdoche of Wisconsin and use it in a sentence, we might be able to use one of the nouns in the question (beer, brats, cheese) to indicate the state. Let's try:

I went to the Cheese State for Thanksgiving.

Do I know that we're referring to Wisconsin? What if I said:

I went to the Beer State for Thanksgiving.

• But the thing about the question is that we aren't actually trying to make a synecdoche for Wisconsin - we're saying that these nouns are a large part of Wisconsin culture that could be synecdoche for Wisconsin. And in that way, the sentence holds up just fine.

• One thing about the sentence though - "synecdoche" is a noun and so should be treated as such. As it's used in the sentence, it's being used as a comparative word. And so I think a tiny edit will do the trick:

Beer, brats, and cheese are pretty much a synecdoche of the entire state of Wisconsin.