What to use to attach copper to stone?
You don't seem to be using the RIGHT mastic, or "construction adhesive". Construction adhesive (ie PL or similar brand name) would be about the best material for the job, because copper is a REALLY DIFFICULT material to bond to.

Try experimenting (with scrap) with other brands or types of mastic/adhesive. Certain types of PL should set up near-hard within a couple of hours.