Dear Tom,
Charles is right. In fact, there are prayer ropes that are divided every ten knots with a larger knot or bead which are used for prostrations i.e. ten metanias and one prostration to the floor.
The rule of the Theotokos can also be said (what you call the "Rosary") and Russians do use it that way.
But you can pray the Jesus Prayer on the Hail Mary beads and just go over the "gaudy" or Our Father bead. Some references say that one may invoke the Theotokos on the Our Father bead "Most Holy Theotokos save me a sinner!"
That's up to you. There is no one rule to say the Jesus Prayer and in Russia the rule for the Prayer can vary from monastery to monastery.
And ultimately - beads are beads are beads.
Alex