A lot of folks, after setting intonation then marking base location, use a piece of double sided tape to place between the bridge base and body. A few others will pin them (install 2 studs in the body and 2 corresponding holes in the bridge base.

I've got 3 GreTschs, all w/floating bridges and am content. Usually perform all string changes one at a time anyway.

On the 512x series, many have found the bottom of the base isn't contoured well to the body, so they'll gently sand it w/a piece of fine sand paper laid on the body in the appropriate position. Improves contact area.

Many are also replacing the bridge itself with a bar bridge for mush better sustain. This I have done on my Son's modd'd 5120 (TV Jones Classics and CTS/Switchcraft guts), and we've been very impressed.