Is it worse than it was with the original bridge? I believe Tokai normally use the type with a "lightning bar" ridge across the top, rather than the plain vintage-style wraparound?
It's hard to know whether it's the bridge at fault or whether Tokai have simply located the bridge in the "wrong" place. I've got a Faber bridge somewhere but never actually tried it out. Given the fact that Tokai and Faber have the same distributors (in Germany, anyway), you'd think they'd work together!
The only thing I can think of is trying TonePros studs instead of the Faber studs - the posts are a bit thinner so they'll give a little more room for adjustment, but perhaps not enough.
Failing that, an adjustable bridge, I guess. There's quite a good choice out there now - TonePros, PigTail, the Graph Tech ResoMax....