How to apply the TO/GA time and EGT limits?
The TO/GA time limit and the EGT limit are hard limits mandated by the approved flight manual. They must be adhered to independently and cannot be traded off between the two.

Takeoff performance is calculated so that if a safe altitude above terrain and obstacles cannot be reached within the time limit, aircraft mass must be reduced rather than the TO/GA time increased.

Having said that, if things don’t go as planned during takeoff e.g. for reasons not known beforehand, I‘d recommend to bust the time limit rather than fly into the side of a mountain, if the choice is only between the two...