Upload to DocLib with jQuery (and REST) without HTML5

Uploading Documents to SP 2013 with jQuery and REST work just fine (Properties when uploading Files using REST in SP 2013) but these methods require a HTML5 compatible browser. The problem is now I also have to target older browsers.

I found a nice jQuery Plugin (https://github.com/blueimp/jQuery-File-Upload) which looks very promising and should do the job. e.g. wrapping in an iframe for older browsers. So I configured it the same as previously but it does not work. I guess you have to provide data as a base64 encoded arraybuffer when using REST. Is there a way to upload a file (can also be witouth REST) to a DocLib, ideally with this plugin?

Configuration:

function initializeUploader() {
    // Init Uploader
    $('#fileInput').fileupload({
        dataType: 'json',
        url: getRESTUrl(),

        headers: {
            "accept": "application/json;odata=verbose",
            "X-RequestDigest": $("#__REQUESTDIGEST").val()
        },

        add: function (e, data) {
            data.context = $('#SubmitButton').val('Start Upload')
                .click(function () {
                    //url = getRESTUrl();
                    data.context = $('<p/>').text('Uploading...').replaceAll($(this));
                    data.submit();
                });
        },

        done: function (e, data) {
            data.context.text("upload finished");
        },

        fail: function (e, data) {
            data.context.text("upload failed");
        }
    });

function getRESTUrl() {
    var serverurl = SPWeb.get_serverRelativeUrl() + "/Lists/TestDocLib";
    var targetRESTUrl = _spPageContextInfo.webServerRelativeUrl +
                        "/_api/web/GetFolderByServerRelativeUrl('" + serverurl + "')/Files" +
                        "/Add(url='testfile.png',overwrite=true)";
    return targetRESTUrl;
}

Errors I receive in the LOGS:

SPRequest.PutFile: UserPrincipalName=[...], AppPrincipalName= ,bstrUrl=http://{myweb} ,bstrWebRelativeUrl=Lists/TestDocLib/testfile.png ,cbFile=38862 ,punkSPFileMgr= ,punkFFM= ,PutFileOpt=1 [...]

System.IO.DirectoryNotFoundException: 0x80070003There is no file with URL 'http://{site}/Lists/TestDocLib/testfile.png' in this Web., StackTrace:

I don't know why SP (obivously) wants to retrieve the file. Previously I also had to specify the target filename and it just worked fine.