The promises associated with saying the rosary are extremely incompatible with Orthodox theology
Quite true. Not all Romans say the rosary for "promises" -- I certainly don't. I say the rosary because it is a means of meditation and spiritual preparation. I don't believe that anything besides worthy preparation in the Sacraments and a life of penance and charity will prepare one's soul for everlasting life.
Nevertheless, I could see why an Orthodox believer would not want to say the rosary simply because Catholics often attach a talisman-like significance to the rosary (they shouldn't). Also, some Catholics place an exaggerated emphasis on the the notion of "promises" and imagination. Just know that there are Catholics who say the rosary in an Orthodox mindset and don't pay attention to the peripherals.
I'm not saying you, or any Orthodox believer, should say the rosary. Stick to the prayer rope. However, the Apostles' Creed, the Hail Mary, the Our Father, and the Gloria Patri are not heretical prayers in themselves.
Quite correct, if we were to attribute pious misconceptions, even ones spread over the years by various Catholic laity, priests, nuns and even Bishops, as being representative of actual Catholic teaching, we need to be prepared when similar misconceptions and misconstructions of our Orthodox faith are spread by our own.
Trevor, please treasure your grandmother's precious Holy cards, icons and religious accessories like her beloved Rosary. Don't become an 'Orthodox iconoclast'.
For example,if you review the beautiful videos posted on youtube by the Patriarchate of Moscow, you will see His Holiness celebrating Liturgy and other services in ancient Churches which survived the Communist era and are full of icons painted in the style of your grandmother's pictures. Check out this one, for example from on Moscow, March 17, 2011. On , Patriarch of Moscow and All Russia, Patriarch Kiril observed the day of memory of the Holy Prince Daniel of Moscow as he celebrated the Presanctified Liturgy at Holy Trinity Cathedral of St. Daniel Monastery. At 1:11, you will see on the rear wall of the Church there is even a carved crucifix with the Body of Christ.http://www.youtube.com/watch?v=4a03uniwp4Y&feature=more_related
There are similar crosses in many old Russian Orthodox parish cemeteries in the northeast erected by immigrants in the early 20th century.