I like your above solution to the problem and as we have a spare ultrasonic it might be worth a try.
A note to the person who said such a pushing force was impossible I don't believe that it is.
http://www.engineershandbook.com/Tab...efficients.htm
lists the coefficient of friction of rubber on solids as being 1-4. That is for a smooth rubber strip on a smooth solid. A coefficient of friction of 2 on carpet is highly possible.