I got a new Charvel a couple of weeks ago, one of the USA-made Telecaster style ones they made a couple of years back. Got it 'new', although it had been in the store for quite a while. Didn't seem abused though, other than a few scratches on the back it seemed in perfect condition. Anyway, was very happy with it.

I restrung it for the first time two days ago and I've now hit a problem. I've got three other guitars with Floyds, two floating and one non floating, and not had this problem before. In fact I've never had any problems with any of them before, I consider myself well versed in setting up Floyds. This one has me stumped though.

When I bend a string normally it ends up going about 6 cents flat, as if the strings haven't been stretched out enough. I'm very thorough when it comes to restringing though and I'm sure I stretched them out properly. This happens to every string, one by one as I bend them, When I dip the bar every string simultaneously goes about 6 cents sharp.

It's not that the bridge isn't returning to the same point. It's non-floating so every time it moves it returns to rest against the top of the body. I don't think it can be the strings stretching because that would only explain them going flat, not sharp. The locking bits at the nut are down as tight as they can safely go. The strings can't be slipping in the saddles either because again that would only explain them going flat. These are going flat, then sharp, then flat again.

Anyone experience this before and know what causes it? I've been using Floyds for about five years now and never had this before.

It IS an American-made OFR.
It IS non-floating, though I did increase the spring tension a little anyway.
I didn't put on a different gauage of string or change to a different tuning.
It's not the intonation I'm talking about.
I don't need a new amp or a set of Bare Knuckles or a new battery or lemon oil
What are you using to block the trem?
On playing the Paul Gilbert signature at the guitar store extensively, my missus sighed:
"Put it down now, It's like you love that guitar more than me!"
In Which I replied.
"Well it has got two F-Holes!"
Sounds like the posts that the knife edges rest on are screwed in too far, or are not the same height. Look at it from the side and make sure the bridge is perfectly centered in the taper. I've seen that happen quite a bit with a non-recessed floyd.
I love all 5 (sold a couple) of my Carvin X-100b's.
I actually raised the posts up a little as I like higher action, but you do bring up a good point. When I got it the bridge was resting on the top of the body on the treble side but the bass side was off the body by a little bit and now that I look I didn't correct that much, the bass side is still very fractionally off the body. Ta. Will even them out and see if that gets it.