De-gloss the tile surfaces one by one with your belt sander and medium-fine sanding belt. Don't attempt to sand off the finish (you won't be able to), but just dull the shine. Clean off the dust with a dry rag.
Brush polyurethane gloss over each tile with a finishing paint brush, using a thin, even stroke in a consistent direction. Don't gloss the grout lines, just the tile surface.
Allow the polyurethane gloss to set for 12 to 24 hours.
Use your extra-fine sandpaper to dull the surface of the polyurethane gloss with quick, light strokes. Wipe up the dust thoroughly.
Apply a second layer of polyurethane. Let it dry, buff it with extra-fine sandpaper, and apply a third coat.
Let the third coat set for 24 hours.