There might also be the option of just optimistically assuming that, for points in a file with a sequence of like >4K bytes of proper newlines with proper comma counts in each, that here probably isn't in the middle of a multiline string, and parsing it as such (of course with proper fallback if this turns out false; but you'll at least know that this whole run is in the middle of a multiline string).

Also, if you encounter a double-quote character anywhere with a comma on one side and neither a newline nor comma on the other, you immediately know 100% whether it starts or ends a string.