An inexpensive fix for that is to order some Graph Tech string trees from Stewart McDonald. They work pretty well. I rarely have difficulties with my strats going out of tune with the bridge floating.
I always lubricate the nut slots with graphite (a pencil works well), and make sure the strings are stretched well when I put a new set on. I keep my action pretty low with 10's at 2/32" of an inch at the 17th fret. With 9's the action usually has to be set a bit higher, but they still stay in tune fairly well for me.
Guitars: 2003 and 2004 American series strats, Squier Classic Vibe 50's Strat, Squier Deluxe Strat.
Amps: Line 6 Spider IV 120, Vox AD50VT 212, and Peavey Transtube Bandit 112.
Pedals: Digitech Bad Monkey.