Locally, I've seen slates turned into coasters (already mentioned) and artistically painted (acrylic? I'm not sure...) as tchotchkes. The coasters have a thin sheet of cork gasket material adhered to them, and have
local interest scenes or sayings laser engraved in them. These are usually for sale near the register of the local grocery stores or in select
gift shops.
Some sort of hot pad/trivet gizmo to protect your fine furniture from hot soup pots and tea kettles (also with a bit of sheet cork on the back side) seems like a passable idea.
I've seen slates stacked on edge on the top of dry laid stone walls as a sort of coping.
https://thestonetrust.org/wp-content/uploads/2013/12/anatomy_top.png
Facing the treads of poured
concrete or gravel-filled crib landscaping steps seems like a possibility. Or, face a thermal mass (top of bench, fireproof hearth area, etc.).
Slates could be turned into sundials/gnomons (engraved or painted hours). Sundials might be a saleable item in local garden centers and greenhouses.