There's lots of good ideas here and for what it's worth, here's my two pennies worth.
Sounds to me that the real problem is a lack of mechanical grip all round. When the grip is low and tyres don't appear to be working, I'd start looking at softening the suspension to allow more weight shift as you'll need to generate traction via weight shift.
so for me, I'd run in the outer link positions in both the front and rear camber blocks (effectively shorter links) as I've found this helps the car to 'generate' traction in slippy conditions.
More front caster will help keep the nose in the turn for longer - I'd run possibly 25 deg kick angle with the stock 10 deg caster blocks.
Raising the inner ball stud height will also keep the car in the turn longer.
At the rear of the car - I'd stand the shocks upright and move them out on the tower - but this will make the car more squirmy. It makes it more reactive but at the limit, it will dump over and feel squirmy.
Less antisquat will improve rear traction as it will enable greater weight shift. If you think you are getting too much weight shift rearward, then try limiting your front shocks as this can be effective.
Rear toe angle is also important. but it's always a balancing act between too much forward drive vs smmother in-turn performance.
All of these changes can be felt but the biggest contributor is most often the tyre + insert combination. I prefer a minipin front tyre to a stagger rib but this is on carpet (and with a mid car). But TBH, I've normally found that I can run more tyre on the front of the rear car than I can with the mid car so I wouldn't be scared to try a minipin front.
If you are running the stock pistons, you might want to try rounding the edges lightly to create a radius between the upper/lower faces and the sides of the pistons. This really helps improve the small bump performance of the shock and makes them more active. If the stock piston is making the car resist roll and keeping it flat then you'll be fighting against it in order to generate the weight transfer during roll that I think you need.
So much to think about but at least it'll be a great excuse to go out a play some more
Like it's been said earlier - try one thing at a time and try to evaluate what the change has made. in all cases, there will also be an opposite and often negative effect also - so you have to think about if the change is better overall or worse - even if it addresses the single issue you are thinking about.
HTH.