What tires are you using and what's the intended use of the car?
It's fine to drive without sway bars. I have 12k/10k on my car and I disconnect the sway bars on the street for comfort. It slightly improves the ride quality and the balance of the car is still fine, although I don't really drive the car hard when I have the street setup on it.
I've found that cars like ours that are designed with sway bars need sway bars to be competitive. I autocross an S2000 in STR and my codriver and I experimented with really high spring rates and tiny sway bars and had some success with it, but found so much more pace in the car by beefing up the sway bars and backing off the spring a little. When we stiffened the rear sway bar and the car started pushing hard we realized that the balance was coming from the rear rolling over on the tire. From there we gained traction on whatever axle we stiffened, so we rolling over on the tire all along despite having very stiff springs.
In your case it sounds like you just need to spend some time in the car and find out what setup is going to work best for the way you drive your car. If there is an autocross group in your area that does test and tunes, that would be a great place to dial in both the car and the driver. I also have an open diff and I've found disconnecting the rear sway does help a bit keeping the inside rear wheel down, but for me it is still a big achilles heel in the car(and a great tool for the driver to learn). It will probably be a bigger improvement for you since that big front sway is going to help keep the inside rear down and you're disconnecting a bigger rear sway bar(mine is stock).