response is all about the ticking clock time between things happening.
You clearly missed the measurement you wanted. Seat of the pants won't help but, if you are on a dyno then map time VS rpm/speed or horsepower to see changes in response.
There are lots of things that can improve it.
Don't know what you are measuring but, generally less time taken to achieve 'x' is what I reffer to as a repsonse gain when power isn't necessarily on the increase. Boost insn't the be all end all.
How much boost you have at 2,700rpm is not really what you want to be measuring, in fact who cares? I think you want a car that accellerates faster and is quick to 'listen' to your right foot. Am I right?
You could bolt a baby single T15 or something on and have more than a bar of boost at 1,500rpm but, your car isn't going to be 'responsive' in terms of performance. Maybe towing another car out of sand.
If we talk just about the GT-SS turbo setup then 'response' improvement could be sensibly confined to the area that turbos works best in with regards to airflow. Removing airlfow restrictions naturally improves the efficiency and speed at which the turbo can pump air.
Can a better designed intercooler acheive this?
Yes. However core volume increases aren't necessarily good if you are chasing better low end/mid range characteristics.
Cams help?
Yep. If the right sized cams are setup with the right settings for valve timing you can bring airflow changes on faster in addtion to pumping more air at the same engine speed. With a reduction in airflow restriction and greater cranking compression if you go more advanced valve timing setting on the intake. You can measure the time it takes to achieve this on a dyno and also power increases are a dead give away.
Anything else that improves response with regards to rotational inertia helps. Light wheels , crank pulley, flywheel & clutch , tailshaft. Diff ratios etc..