Yeah, man.... you have the same issue I had. Well first of all, you really aren't suppossed to resurface a fidanza flywheel. It only costs $50 for a new steel insert and you probably paid almost that much in resurfaceing fees. Second of all, as brian said, there are 2 surfaces which need to be resuraced to maintain the proper drop from the steel disc to where the pressure plate contacts the flywheel. The 2 part is obviously aluminum which can't be grinded down very easily without butchering up the whole flywheel. I did have my fidanza resurfaced on my old setup with my Spec stage 1 and I had them just take a fuzz off the steel insert and none off the aluminum and it worked fine and the disc was still pinched between the pressure plate and flywheel. It defenitly should not be loose like you are saying. On my most recent build, when I was using the Spec Stage 3+ like you are, I bought a new insert for my flywheel for $50 and I put it together and the clutch disc was sloppy as can be. I couldn't figure out why until I later figured out that the clutch they sent me was for the zetec! Everything fit together, but the only difference was that they pressure plate had a different offset than the duratech pressure plate. I came to find out that both the zetec and duratech use the same clutch disc, just the TOB and pressure plate are different. Call spec and verify the part number to make sure that it is not a ZETEC stage 3+ kit. If it is, then that is probably your main problem. If it isn't a zetec clutch kit, then you must have had wayyy to much taken off your flywheel and you need to buy a new $50 insert. I would almost replace the insert no matter what because I would think it would be better for the longevity of the clutch to have the new flywheel insert. When I pulled my stage 1 that had been used against the fidanza flywheel that had been resurfaced, it didn't look like to good of wear. PM me the part number of your kit as well and I will check to see if I have any photos of the zetec kit they sent me.
Good luck.