I have 19" Michelins and no PASM - the car feels very firmly sprung but not crashy and very well damped. I drove a 19" car with PASM on a test drive plus (but can't remember the make of tyres) and it felt too hard and not particularly well damped although at the time, I'd never driven a 987 and thus could only really compare it to my old 986 on 17" contis.
I've driven my car pretty enthusiastically on the road (not yet on the track) and I absolutely love the feeling of it particularly through fast, sweeping A roads. I can't believe anyone could call it "floaty". My last sports car was a Caterham Superlight so my experience is with a far more direct and involving car - even so the Boxster chassis is amazingly well controlled.
I'd suggest that there's something amiss with yours - perhaps the tyre pressures, a tyre out of true, poor alighnment, fulty damper or somesuch?