And it is hard to disagree with those who argue for the concept of the override button...
any override button has to be certified as "safe" not exceeding limits, else the FARs need to be changed (not in our lifetime).
OTOH you can always opt for a "reserve thrust" option on an engine, which means it is certified for birds at that condition and then takeoff normally with less than reserve thrust and after ingesting birds you can have a big red button to push.
Or if it's EGT/TIT overlimits that really is part of your concern you can mandate the maximum allowable deterioration of an engine on-wing such that even after a bird ingestion you have lots of margin.
sorry there is no quick practical solution just multiple contributors to pick at.