Spreadsheet string to Array doesn't care about the quotes. Make sure you use a comma as the delimiter.
But every element in your first column will start with a quote, and every element in the last column will end with a quote. What you can do is use some string subset functions to remove the quotes from those elements after the fact.
If you don't expect a legitimate quote to ever be in the file, then you could search and replace all quotes with nothing before you turn it into an array.