Dave,
Two thoughts and a comment:
1) Oak is porous, and that might be an issue for keeping it clean
enough for food production.
2) Careful with glues, in case there is any issue with toxic gunk or tastes getting into your cheese. I'm not sure what sort of glue is used for pizza peels, but maybe that would helpful to know(?)
Many woodworkers consider all finishes to be food safe after fully cured, but I'm not entirely in that camp. When I make bowls intended to be used for food, I use Tried & True Original -- polymerized linseed oil and beeswax, with no solvents, driers or anything else. Not very tasty, but you could eat it right out of the can without poisoning yourself.