No tremelo I've seen can keep perfect tune, but it sounds as if yours is giving you more trouble than it should. I don't own a floyd rose, so if you say it looks fine then I'll believe you. i've got one question: did you stretch in your strings when you put them on? If you gently stretch each string by putting your index finger point on the fretboard and using the other fingers to pull the string away from the neck, at each fret, the strings will tend to stay in tune better afterwards. Strings need time to settle in, as the tension on fresh strings will stretch the metal a bit and send them out of tune. A tremelo will send new, unstretched strings out of tune very quickly.