Is it possible to upgrade a Boeing 747-8 and Airbus A380's engines for greater speed?
I just wanted to comment on this question since some of my code is on the A380's GE engine.

Those engines are optimized for fuel efficiency at their cruising altitude and speed.  The tradeoff that you fight against when designing the engine for cruising altitude is that it makes the engine hard to start, and the stall margin (the pressure and fuel combo you need to keep the engine from stalling) is razor thin when they are on the ground.

Just to echo what Kevin said, any improvements to allowing the engine to start without stalling would surely go to the fuel efficiency, not to speed.