I've spent 13 years modifying my car to handle better on the track. The transverse TTV6 isn't the problem but the differentials are.
The Evo's are known for it's good handling has a very similar engine layout but much better diffs and we all know how they handle.
Among all the modifications I've done to my car (big brakes, Öhlins coilover, DR750 etc) I've replaced all 3 diffs on my car one by one and the car behaves completely different now.
The stock viscous center diff is too weak and too limited in it's ability to redistribute torque which make it unsuitable for track use. On winter road it may work fine with it's 45/55 torque distribution but when your putting the power down on the track if one axle starts to spin it will keep spinning because the viscous center diff is unable to transfer more than 50% of the torque to one axle.
So I started by installing a Supercar torsen center diff with it's 20/80 front/rear torque distribution and it really changes how the car behaves on tight tarmac tracks. The on throttle understeer heavily reduced and the car behaves much more like a rwd car. It also makes the behavior of the car much more consistent since the mechanical nature of the torsen diffs makes it much more predictable and faster in it's reaction compared to the stock viscous center diff.
Here is a video I made that shows how rear wheel biased the Supercar torsen center diff really is.
https://www.youtube.com/watch?v=fTQEldXlCDc
Even with the 80 of the torque going to the rear wheels I could still get the inner front tire to spin a bit when exiting tight corners as seen in the clip below. I cured that by installing a Quaife front diff which essentially removed all traces of on throttle understeer when used in combination with the Supercar torsen center diff. I ran that setup with great success at many events for a while.
When I upgraded to DR750's and water/meth injection I started having problems with the inner rear tire spinning wildly during acceleration out of some corners due to the weak stock rear LSD in our cars. Here is a video of that:
https://www.youtube.com/watch?v=a0saF10a-94
I ended up replacing the rear differential with a Mitsubishi torsen/visco hybrid diff that after a rebuild has worked great and the rear really stays planted now during acceleration.
Here is a video from an event a month ago that shows how the car drives now (fastest run is at the end).
https://www.youtube.com/watch?v=9YTso_nYFv0
As you can see the car tends always oversteer except in the really really tight breaking turns. During oversteer I can usually just keep the foot down and counter it easily which makes the car easy to drive on the edge for great lap times. However it doesn't always go as planned as you can see in the video above.
I run Öhlins coilover with SCE adapters on a very low ride height and 265 tires on 9,5 rims. I have 2.7° of camber in the front and 2° in the rear. The front camber is really important on these cars else you will eat up the outside of tires quickly and overheat the tires.
I've attached a few photos of how the car sits on the track.
I don't think the on throttle behavior of our cars can be changed significantly without replacing at least the center differential.