The only thing to do in this scenario (high rate of climb at high alt, and increasing speed) -which an experienced airbus pilot will tell you - is to press VS0, and select a lower speed eg. .76.
This will arrest the climb and level off the A/C. (You might have to press VS0 a few times, if the a/c is already in ALT* (or ALT aquire in Boeing lingo.)
Then when the a/c has regained its composure you select V/S climb with a low rate eg. 500 fpm and monitor it closely as it creeps up to level.
(The rate of course depends of the weight and thrust rating of the A/C).
This way you avoid the drama of a high workload situation involving speed brakes, closure of thrust levers etc.
As a note. These comments are not intended to put down the individual involved in the situation.
He/she found himself in an unfamiliar situation that developed rapidly, and tried to cope as best as possible.
The rest of us can take note and learn....