No, most mosses are not sheet-forming. Sheet mosses will come up in a big piece when you pull them up, like sod; other mosses will crumble apart. The sheet moss in my area has fern-like fronds about 1" long; there are other sheet mosses in different areas. You can also order sheet mosses from various places.
Sheet moss or liverwort will probably be your best bet for the slate; you can hot glue the sheet moss on (just a few dabs of glue). To start your liverwort you will just have to find a rock with a bunch growing on it already (look along the edges of small woodland creeks) and place it beside the slate; eventually the liverwort will spread onto the slate. Some liverworts have broad flat thalloi, while others look like glossy mosses.