How to Post Google Forms Data via jQuery and Ajax to Spreadsheets

I'm working on a Chrome extension that's essentially a simple custom Google Form that will post to a response Spreadsheet. I got the following function to successfully send and populate data only once, but never again:

function postFormToGoogle() {
    var timeOne = $("#time1hour").val();
    var timeTwo = $('#time2hour').val();
    var timeThree = $('#time3hour').val();

    $.ajax({
        url: "http://ift.tt/1CZOL0U",
        beforeSend: function (xhr) {
          xhr.setRequestHeader('Access-Control-Allow-Origin', 'http://chrome-extensionEXTENSION_ID');
          xhr.setRequestHeader('Access-Control-Allow-Methods', 'GET, POST, PUT');
        },
        data: { "entry_856586387": timeOne, 
        "entry_244812041": timeTwo, 
        "entry_2138937452": timeThree },
        type: "POST",
        dataType: "xml",
        xhrFields: {
            withCredentials: true
        },
        statusCode: {
            0: function () {
                document.getElementById("message").innerHTML = "Your form has been submitted!";
                window.location.replace("ThankYou.html");
            },
            200: function () {
                document.getElementById("message").innerHTML = "Your form has been submitted!";
                console.log("Success");
                window.location.replace("ThankYou.html");
            }
        }
    });
}

I had to include the cors request headers because I was getting a No 'Access-Control-Allow-Origin' warning that blocked my request.

It being an extension, I also added the following permissions to the manifest.json file:

"permissions": [
  "http://docs.google.com",
  "https://docs.google.com",
  "https://*.google.com",
]

At this point, I'm not sure exactly what's preventing the data from posting. Possible indicators could be that when submitting the form I'm getting a "Provisional Headers are shown" caution and the server is taking way too long to respond as indicated by the Waiting (TTFB) time.

Where am I going wrong in the code? (It did work once, for some reason.) Any alternative solutions out there to post a custom form to Spreadsheets?