I have an adjustable front sway bar but this will only help to minimize push in mid turn (which these cars are prone to do).
My GTS is lowered, yes. Problems in transitions like you describe are usually correctable by changing the shock settings.
If your shocks are adjustable for bump and rebound (which I think you indicated above) you can play with these settings.
For a quicker weight transfer on turn-in, you would want to decrease the compression setting (resistance) on the outside wheel (and/or decrease the rebound setting on the inside wheel).
Also, the shock settings will affect the effective corner weighting while cornering (as opposed to static corner weight).
This is complicated business. Considering that shock settings, ride height, spring rates, sway bar stiffness, camber settings, etc. all interact with each other, it's no wonder that professional teams spend megabucks testing and adjusting.
I think this is part of the fun of tracking your car and helps me to learn about all these suspension parts and their effects on handling.
Taking tire temps though is the ultimate measurement of the appropriateness of your settings.
Good luck and have fun!