Having had a severely bird-damaged engine, my experience was that to stop severe surging the throttle had to be retarded to about 1.3 epr (old fashioned engines ). Any attempt to advance throttle resulted in surging and instability with an apparent loss of thrust. FADEC or not, once the mechanicals are damaged, more fuel will not necessarily mean more thrust, it may just put you back into a zone of instability.
By the way, the reason a badly damaged engine was kept running was because both engines ingested birds and surged massively, so the "good " one had unknown damage, and we might have had to survive on the "bad" one.
On subsequent inspection the "good" one had blood and feathers from several ducks, but was otherwise undamaged, but the bad one was a million dollar write-off.
PS the monday morning quarterbacks pointed out that we might have gotten a little more thrust/stability if we had turned on the anti-ice bleeds. At 30 Celsius OAT we overlooked that. Nobody's perfect!