Most Orthodox peoples objections to the Rosary have nothing to do with the prayers. It has to do with the "mysteries" that one is supposed to meditate upon while reciting the prayers.
Please note that the word "mysteries" in this context is very different from our usage of the term "Mystery" or "Mysteries" when referring to what might also be called a "Sacrament" (ie. Baptism, Holy Communion, etc.). In the context of the Rosary, a "mystery" is an event in the life of Christ, His mother, or the Church, which one mulls over in their mind. I'm not exactly sure what the precise explanation is since I was never a member of the Roman Church, but I think that's the gist of it.
What is repeatedly warned against, rejected and condemned in the writings of the Fathers is the use of imagination in prayer. When we pray the Jesus Prayer, what we are to focus our minds on is the meaning of the words of the Jesus Prayer - "Lord Jesus Christ, Son of God, have mercy on me, a sinner". Simply, we stay focused on what we are praying, rather than letting our minds wander about, even if it is within a paticularly pious subject like one of the Rosary mysteries.
That's why some people say the Jesus Prayer faster than others. What you need to do is find a pace that is fast enough that it doesn't let your mind wander in between prayers, and yet slow enough that your mind doesn't wander away while you're pronouncing the Jesus Prayer and not thinking about it, like some sort of mantra. Rest assured though, finding that "in between" and keeping your mind focused is hard work!
Plus, any other stuff that gets mentioned in things like the Philokalia are usually for far more advanced monastics than any of us. If you ever do read the Philokalia (or excerpts from it) remember that the term "beginner" or "novice" there means someone who has recently been tonsured into the Great Schema and started living as a monastic hermit! It is most definitely not you or me!
Now, I know there are some Western Rite Orthodox who make use of the Rosary, but I'd have to let them speak as to how they reconcile it with the prohibition of imagination in prayer. My guess would be that they would somehow distinguish between meditation and imagination, but I'm not sure exactly how that would work. I know some pray the Rosary sans mysteries, which seems a perfectly good idea to me. I also know that some WR types are thoroughly opposed to the practice. Nonetheless, I should refrain from putting words in their mouths. Hopefully they'll be along shortly to speak for themselves, and I offer them my apologies in advance if I've misrepresented anything.