Heavy, low cost heat storage options are possible with stationary systems.
In a heat storage system the steam turbine only runs to charge a small battery. This battery only holds a buffer emount of energy to prevent power loss when many loads are turned on at the same time or fast on off cycle with the turbine. When loads are turned on the battery quickly discharges to a certain low level. The stored heat is then used to run the steam turbine and charge the battery. When an upper lever is reached the turbine is shut off. Virtually all the energy stored is in large heat storage tanks.
These can easily be homemade by filling an oil drum with rocks and pumping oil through the rocks to add or take heat from the tank. The oil drum would then be well insulated with something like fibreglass insulation. The cost of this storage system per KWH would be much less than buying batteries. Also this system has no drop in performance with high cycles.