What can be used safely (e.g. basalt "hot stones") to fill volume of shallow pan for deep frying?
It's a neat idea and basalt is definitely a solid at 1000°C and is only a fluid liquid at 1200°C, so it's quite safe except it takes more time to heat up basalt than oil...  So the oil you're going to save while using a large pan containing basalt is going to be offset by the extra energy you need to pump into the system.¹


On a camping site when you don't have enough oil? Yeah, go for it!
In your own kitchen? Up to you, but I would just buy a smaller pan.


Note¹: Basalt is volcanic rock and also takes more time to cool down, so be careful when you do use it; leave the pan overnight on your counter to allow the basalt to cool off...