I think it is the QR slipping in this case. If it starts off like that, it's probably from the initial momentum and stress on the freewheel that pulls it forward, but once it starts rolling 'corrects' itself. My guess would be to try and go to your local bike shop and pick up a QR skewer for $10.

I don't think tensioners would work in this instance, with the frame you have, although I stand to be corrected. Another route is that you can have the QR axle replaced with a bolt-on one.