Hm
Too much writing about all but facts.
Overloaded or not would have hardly changed anything !
On that altitude there may exist ice particles...
but hardly any ICING for wings or engines.
And because pilots DISCUSSED whether or not use de-icing ONLY proves the above.
However ice dust is absolutely harmless to engines and whole aircraft .....
it is can sometimes be very NASTY to PT2 signal, if Engine Anti Ice was NOT switched ON.
PT2 probe can get filled/BLOCKED with ice dust, now, its signal would change so
that pilots indicators for engine thrust (EPR, either left or right or both)
would start INDICATING HIGHER thrust (another words giving false indications),
and even much above max limit.
As in any normal operation, the ATS (AutoThrotlle) would be on, it would tend to "reduce" thrust to MAX Cruise EPR (or whatever EPR was selected on TRC),
thus ACTUALLY reducing (TRUE) thrust EVEN to IDLE, while pilot's eyes would be "happy" with "MAX" power selected.
(Actually seen few times in climb and cruse.)
For all else, please read what has happened in the cockpit, from top FL to ground.
Cheers
G.G.