How indeed would the Orthodox meet the objections of Protestants who claim:
1) "Christ is only spiritually present."
See above "this is indeed your most pure Body, and this indeed your precious Blood." It's a plain statement, the simplest grammar in any language I'm aware of: x is y. Period.
2) Catholics and Orthodox are practicing cannibalism in their Eucharist.
My response would be 'so?'. If it *is* the Body and Blood of Christ, then it can only be so through the direct action of the Holy Spirit. If Christ commanded it and the Holy Spirit chooses to give it to us, who are you (i.e., generic Protestant) to criticize?
Ponder your responses, and I think you will discover:
1) It is not as simple as simply claiming "Christ is present";
True, for Orthodox it's simpler. It's not even a matter of 'Christ is present', it's that the Eucharist is the body and blood of Christ.
2) the necessity of being able to explain the matter in a logical and coherent manner;
I think this actually gets at the crux of the difference between Orthodox (Oriental or Eastern) and RC here. The Eucharist is a transcendent Mystery (in the original sense of that term). We don't see a 'necessity' to explain it; like 1=1 in Math, 'it is the body and blood of Christ' is an axiomatic statement.
That said, Orthodoxy has not, generally, had a problem with Transubstantion. We don't embrace it, as the Roman Church does, simply because it is based on Thomist/Scholastic philosophical categories that we do not necessarily accept. Or to put it another way, *if* you are going to assume a Thomist philosophy, then Transubstantion is a perfectly valid explanation of the Eucharist. And therefore, an Orthodox can define our belief as 'Transubstantion' (as, for example, the EI Council of Jerusalem). It's just not required to define it that way, since the underlying philosophy/categories/vocabulary is not required (or even generally accepted)