With excess solar you usually just detach the inverter. In some areas, like Southern California, this can be forced during peak solar times.
As for the price going negative - this isn’t a super new phenomenon. I remember learning about coal power plants in West Virginia having negative power prices in the late night. This is simply because it’s hard to spin down and scale up these loads. It’s more cost effective to pay people to take the energy for a short time than it is to shut down the plant and potentially destabilize the grid in the future.
As for sinking it into the ground - there’s lots of research there. Tesla is pushing utility scale batteries. Other efforts move large rocks up and down hills, convert water to hydrogen and oxygen, or simply pump water up hill. Each of these has some losses and hardware costs to get going and efficiency isn’t great.
At a home you can get a set of Tesla Powerwalls and essentially do this - but you’ll find they cost about $6k each and eat about $7/mo in electric losses (at the $0.23/kWh price I pay - thanks, Eversource).