What confusion you must see in our attempts to answer your question!
E.g., Communion with the monophysites mentioned earlier would place those who entered into such communion outside of Orthodoxy... but that would mean that many in North America would be outside of Orthodoxy!
No, no, our answers as Orthodox Christians are never up to par if you need rational proof of one's position, almost as though you could "prove" your case in a nearly-scientific investigation. No, we Orthodox have but faith and history on our side: both of which can be bent and distorted (many times unconsciously, of course).
I too was a seeker not too awful long ago, having realised smack dab in the middle of a year at Bible College that I couldn't be Protestant anymore (for doctrinal reasons). So the search began, to the liberals and cafeteria Christians, then to the traditional/historical Christians. I became Orthodox, though it was quite a struggle to do so. And now you are in the same boat perhaps, and are thinking about switching to our boat, but you think you've spotted a couple holes in our boat.
Well what can I say? Maybe we do have holes in our boat. Jesus Christ promised that the gates of hades wouldn't prevail against the Church, he never said that the Church would be invincible. The sobering phrase "the world woke up and found itself to be Arian" (to paraphrase) comes to mind.
And so how does one demonstrate the validity of Orthodoxy? Do we give you all the arguments, historical and theological, that we
found persuasive? No, that stuff is already easily findable on the web, apologetics and expositions on such matters are easily found. (I would only mention one page, that dealing with the differences between Catholicism and Orthodoxy
Perhaps the most helpful thing I can say is: look around for yourself. But don't ask "what do they believe," don't be like Pilate and focus on the "what". "What truth is" will come in time, but it is the last step in the road. This is what most people stumble on, because they want to know all of the "what," and then decide which group best lives up to that truth. We as humans need to do the opposite, though. We need to first ask "Who is truth?" It's not that we don't have any idea what the answer to "what is truth?" is--certainly we can figure some things out even if we've never even heard of Christianity or Christ--it's just that we can't be sure that what we believe to be truth is truth, and so we must start with He Who IS Truth incarnate.
After we determine the Who, we must ask "Where is truth?" In other words, where does the Who reveal the truth? What is a "truth telling thing" (to borrow the phrase of Chesterton)? We are not asking "what comes pretty close to getting it"! We are instead thinking here: "Where did Christ designate as the place through which He would reveal Himself?" After the where, understanding the Why and What would come next. But again, the Who and Where must come first, or we will have everything backwards.
I'm sure you can guess how the Orthodox Christian would answer all these questions, so there's no point in giving a long discourse as to our answers. All I can say is that I hope you ask the right questions, and seek to find the answers not only intellectually, but also experientially, for man is made of both a body and a soul, and without either he is not a man (so we must not neglect either on our spiritual journeys). May you find He who is the truth, and that place at which you may find the truth!