Barring any theological innovation by the EP, and a resultant non-communion of some or all of the remaining Orthodox Churches, Moscow has no chance whatsoever of filling the role of the "third fiddle" so to say.
But we must understand that the EP's primacy is only temporary until such time when the Vatican (from an Orthodox point of view) returns to Orthodoxy, theologically. The EP is "first in honor" only by default (non-communion with Rome), since the primacy of Peter is established by the same Ecumenical Council.
If, for example, the Turks decide to close or bulldoze the premises of the tiny EP's parish, his office remains and the honor of that office retains all the privileges, regardless if what is physically left of Constanitnople is but a heap of lumber and bricks.
The next Ecumenical Council may very well consider granting Moscow the status of the "3rd Rome," because of the size of its jurisdiction, just as Constantinople was elevated over other older Churches simply because of the city's imperial significance (as was Old Rome for that matter). But such elevation of the MP could not be a hostile act of demoting the EP any more than the establishment of the EP was a hostile act of demoting the Pope (which it wasn't).
That said, the EP was not always right, and needed to be corrected. One example, for instance, is the (in)famous Pat. Meletius IV (Metaxakis), who opened a wound that is still wide open and sore, of introducing the "New Julian Calendar" (he didn't introduce the Gregorian Calendar), and who actually recognized Anglican orders and at one time proclaimed Anglican-Orthodox union (of course no other orthodox Church did!).
But he also showed, as did the current EP, some jurisdictional ambitions, having absorbed the Orthodox Church of Finland (whose calendar in uncanonical, by the way, because that Church celebrates Pascha according to the Catholic calendar, and apparently with EP's blessings), which was jurisdictionally under the MP.
The laity must be very much aware of personal corruption among the clergy, especially the senior clergy. Considering that they all come from monastic ranks, such wanton ambitions and power hungar is wholly unacceptable and highly damaging to the Church.
"One example, for instance, is the (in)famous Pat. Meletius IV (Metaxakis),"
The guy was a nut.
"The laity must be very much aware of personal corruption among the clergy, especially the senior clergy."
And the laity must "BEware!"
"The Ecumenical Patriarch is, of course, correct when he asserts that any serious talk of a "3rd Rome" (i.e. Moscow) is uncanonical."
Just like the Pope is right when he says the 4 ancient sees were all heretics right?
Orthodoxy does not understand a primacy like Rome's. There is no primacy that gives the right to arbitrarily interfere into the sees of orther Patriarchates.