What the other said. I use #12 sheet metal hex head screws, just easier for me to install/remove with a power bit. Most of the time mine go about an inch into the wood unless it is a platter or some other slim item.
Do try to have a flat area to mount the faceplate to, it can even be a little concave but never convex. Even if you start between centers (spur drive) and only flatten an area big enough for your faceplate it will help a lot (You can remove the little nub with a chisel). My faceplate is 3" so a 3-1/8 forstner bit works fine, I think your faceplate is quite a bit larger.
Keep tailstock support until it is fully rounded as best you can.
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