[trosc]

Why not let website visitors make your measurements by loading the JavaScript files from the CDNs in the background?

Something like (untested):

    var i = 0;
    var urls = [
      "http://cdn.jsdelivr.net/jquery/2.0.3/jquery-2.0.3.min.js",
      "http://code.jquery.com/jquery-2.0.3.min.js",
      ...
    ];

    function measureRemaining() {
        if(i >= urls.length) return;
        var url = urls[i++];
        measureLatency(url, function(latency) {
          // TODO: post (url,latency) to back-end
          measureRemaining();
        });
    }

    function measureLatency(url,responseFn) {
        var script = document.createElement("script");

        // Bust through browser cache
        script.src = url + "?bust=" + Math.random():
        
        var start = new Date().getTime();
    
        script.onload = function() {
            var end = new Date().getTime();
            var latency = end - start;
            responseFn(latency);
        };
    
        document.getElementsByTagName("head")[0].appendChild(script);
    }

    measureRemaining();

In this way, you'll get actual end-user performance from a (hopefully) large number of different network locations. You will probably want to do this in a separate iframe to avoid changing the behaviour of your webpage.