The floating feel is often struts & shocks. A crude test is to push down on each corner in an attempt to bounce the car, looking for the correct damping which makes it return to normal ride height without bouncing. Not conclusive, but if the struts (front) or shocks (rear) are that bad, it should feel loose and you'll be able to maintain an oscillation.

Lifting each corner is best to determine what if anything is loose. Play in steering components can be dangerous, and visual inspection as well as the push-pull test for play in each joint is really necessary at this point. A good mechanic will check it over thoroughly.

How is the tire wear?

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Gone to the dark side

- Jeff