I asked Comsol for the eigenfrequencies of a simplified PMC body. The outer dimensions are as in the design document (6.89″ × 2.375″ × 2.00″), and the borehole has a uniform diameter of 1.188″ (instead of stepping down to a smaller diameter part-way through the body).

Comsol says the lowest mode for silica is at 8.3 kHz, and for stainless steel the lowest mode is at 7.2 kHz. For this simulation the body is assumed to be completely free; I didn't add 3-point contacts or anything like that.