Split using delimiter except when delimiter is escaped

I'm reading clipboard data coming from excel using

var stream = (System.IO.Stream) ( Forms.Clipboard.GetDataObject() ).GetData( Forms.DataFormats.CommaSeparatedValue );,

but unfortunately, excel is passing cell text instead of cell values. When the cells are using special formatting (such as the thousands seperator), the clipboard data for a series of cells in columns that looks like this:

 1,234,123.00    2,345.00    342.00      12,345.00

is stored as this:

\" 1,234,123.00 \",\" 2,345.00 \", 342.00 ,\" 12,345.00 \"

when what I really want is this:

 1234123.00, 2345.00, 342.00, 12345.00

I had been previously using the clipData.Split(new string[] { "," }, StringSllitOptions.None)) function to turn my CSV clipboard data into a series of cells, but this fails when there is escaped formatted text containing commas.

I'm asking if anyone can think of a way to split this string into a set of cells, ignoring the commas escaped within the \" bits, since this is how Excel is choosing to escape cells containing commas.

In short, how can I turn a single string containing this:

\" 1,234,123.00 \",\" 2,345.00 \", 342.00 ,\" 12,345.00 \"

into an array of strings containing this:

{ "1,234,123.00", "2,345.00", "342.00", "12,345.00" }

Without ruining my ability to parse a simple comma delimited string.

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Follow up question (formulated as a DFA) here: Split a string based on each time a Deterministic Finite Automata reaches a final state?