Unit Testing Angular Service that uses $timeout with Jasmine's Mock Clock

I have a function inside one of my angular services that I'd like to be called repeatedly at a regular interval. I'd like to do this using $timeout. It looks something like this:

var interval = 1000; // Or something

var _tick = function () {
     $timeout(function () {
        doStuff();
        _tick();
    }, interval);
};

_tick();

I'm stumped on how to unit test this with Jasmine at the moment - How do I do this? If I use $timeout.flush() then the function calls occur indefinitely. If I use Jasmine's mock clock, $timeout seems to be unaffected. Basically if I can get this working, I should be good to go:

describe("ANGULAR Manually ticking the Jasmine Mock Clock", function() {
    var timerCallback, $timeout;

    beforeEach(inject(function($injector) {
        $timeout = $injector.get('$timeout');
        timerCallback = jasmine.createSpy('timerCallback');
        jasmine.Clock.useMock();
    }));

    it("causes a timeout to be called synchronously", function() {
        $timeout(function() {
            timerCallback();
        }, 100);
        expect(timerCallback).not.toHaveBeenCalled();
        jasmine.Clock.tick(101);
        expect(timerCallback).toHaveBeenCalled();
    });
});

These two variations work, but do not help me:

describe("Manually ticking the Jasmine Mock Clock", function() {
    var timerCallback;

    beforeEach(function() {
        timerCallback = jasmine.createSpy('timerCallback');
        jasmine.Clock.useMock();
    });

    it("causes a timeout to be called synchronously", function() {
        setTimeout(function() {
            timerCallback();
        }, 100);
        expect(timerCallback).not.toHaveBeenCalled();
        jasmine.Clock.tick(101);
        expect(timerCallback).toHaveBeenCalled();
    });
});

describe("ANGULAR Manually flushing $timeout", function() {
    var timerCallback, $timeout;

    beforeEach(inj