To inject lot power in sand without overheating the vicinity of the resistance :My point is you have to operate the heater at a temperature it (and the sand) can handle.
If only raising to 100C maybe 200C, fixed power could be OK.
Raising sand to 600C, depending on conductivity, temperature of the element may rise as the drum of sand gets hotter, so tapering to a lower final wattage would allow faster heating earlier. Otherwise, a constant reduced power.
You can experiment, see if you wreck elements. My guess is they will get too hot if powered with 240V and buried in sand. It might come out encased in glass, and/or it may fracture.
The stove control may simply be a dimmer switch. That or a light dimmer would be a good way to test power vs. temperature.
1 - Increase the number of resistances : my wife is a ceramiciste and there are like 3m/4m of twisted wire for a pretty small furnace
Wire look like this :
This pack .. cost 350€, but it heat ceramic to 1300°C, and they do not last long => higher temperatures also mean more expensive maintenance.
Firestone/firebrick are used in first layer in contact with the high temperature material.
2 - Decrease power
As an example i can send 3.6kW in my water tank without any problem (i use dead water), i got 2 x 3 resistor (600W each), i use solid state relays to switch them on depending on the available excess pv power, controlled with an arduino ( i got 8kWc of pv).
Switching to an other thought, heating a thermal mass (with sun power) the whole summer to use it in winter is not .. that usefull, periodicity is too important. It would be like going on a 15 days hike and taking all needed water for the trip while there are a lot of places to take water on the path. My system deliver 12kWh on a sunny winter day (35kWh in summer).
Slowly storing a lot of energy for late use will lead to a lot of loses, taking that as a quality, the easier solution would be to put the sand tank in the middle of the house with enough insulation to let him radiate what needed to keep the house at the right temperature for an average day of winter, just let it radiate.... add a simple sleeve over it to have a little control of the output.