For high voltage substations, the NESC applies.

The objective with a substation grounding grid is to limit the step and touch potentials - the voltage a person is exposed to while a fault is flowing to ground. I checked the figures in the OP and came up with a very similar total resistance using a spreadsheet I developed from IEEE 80. My cacls show you would need to lower the soil resistance to about 160 ohm-meters to get to 4 ohms. You should be able to treat the soil and get the resistance down into that range.

The maximum allowable resistance is a function of the available ground-fault current. With approximately 6 ohms total resistance, your step voltages are within tolerances up to about 12,000 amps of available fault current. With a 4-ohm grid, the tolerable ground fault is about 18,000 amps. If you know the availble fault current, you may be able to use the IEEE 80 methods to show that your system is adequzte at 5.95 ohms.