Consider core drilling, and what can be achieved.
The material is soft, and progress should be fairly rapid. If you find nothing, you could fill the cavity with plaster or cement. What harm is there in do that?
4 teams of core drillers, one group for each side. Drill 1" holes reaching 375 ft. As you progress upwards, the length would become less and less. Because the Pyramid has steps, putting together a wood platform, will allow you to reposition yourself 5-8 ft higher, each time. The equipment is manageable.
There is nothing cheaper and more effective than this approach. They would instantly know if they hit any kind of a chamber, and send in a camera. It also would put an end to Houdin spiral nonsense.
Why they choose not to do this, in an organized fashion, bewilders me.