Get a tire with a higher speed rating. Although you may never drive at that speed...the higher speed rating is proportional to the overall tire stiffness. Part of the reason you're feeling that disconnected ride is the soft tire structure.

As someone else suggested, new shocks will also get rid of the floaty feeling. Even new OEM shocks will do wonders. Aftermarket OEM's generally tend to focus on performance, and ride quality/comfort take a back seat. So if you go with aftermarket parts, realize that you may be making some tradeoffs.

Lastly, take some time to play with the tire pressures. About 3 psi up and down from the recommended pressure in your owners manual should give you a good idea how the car handles over a range of tire pressures. Adjust to suit.