Oh, that's such an old, lame James White argument. [sigh]
First of all, everyone at the Council of Chalcedon believed in the real presence of Christ in the Eucharist. Should we believe that they set out to contradict their own beliefs? Of course not.
Second, being "in thousands of places at once" is not "omnipresence," which is a divine attribute, but multilocation. I think Christ's glorified body is perfectly capable of multilocating, just as it was capable of walking through walls and doors.
If the claim is that this "tissue" is truly from the body of Jesus Christ, then it is either his pre-glorified body - which was what was broken for our sins, and blood - which was shed for our sins, or it is Jesus' glorified body which is seated at the right hand of the Father in heaven.
The humanity of Jesus Christ in the Eucharist is certainly his glorified humanity. As to what you see in a Eucharistic Miracle ... the definition of a miracle is a manifestation encouraging faith which cannot be explained by natural means. Beyond that, it's hard to tie down.
People asked me for a miracle. There are lots of miracles associated with the Eucharist.
Which is simply an opinion and does not have any Scriptural support at all.