The argument you're bringing up -- that transubstantiation contradicts Chalcedon -- was lodged by John Calvin. His argument is that transubstantiation makes Christ's humanity omnipresent, thus contradicting Chalcedon, because omnipresence is an attribute of divinity, not humanity.
Of course, there's the simple answer that the Council Fathers of Chalcedon unquestionably accepted the Real Presence of Christ in the Eucharist (a long list of proofs can be adduced for that), so they must have been contradicting their own belief, as well!
However, Calvin's premise is wrong, so his argument collapses. Transubstantiation does not make Christ's humanity omnipresent (present everywhere) but merely multipresent or multilocal (present in several places at once). That's not the same thing.
And, there is no reason to suppose that glorified humanity cannot be multilocal. (After all, according to the Gospels, it can pass through walls and doors, so why can it not be in two places at once?) In fact, there are thought to be cases on record where non-glorified humanity is bilocal, through a miracle. The Italian stigmatist friar St. Pio of Pietrelcina (Padre Pio) is believed to have had the spiritual gift of bilocation, for example.
Six of one, half-dozen of the other. The issue isn't between whether he's omnipresent or multipresent, but rather that neither is a characteristic or ability of non-deistic beings. There is no record of the multipresence of angels, nor is there record of multipresent humans. The understanding of Christ's ability to pass through walls and doors is speculative and not explicitly stated in the text.