Is there a Grounding Electrode that can be buried less than 18"?
You need to talk to your AHJ

(Authority Having Jurisdiction, i.e. The guy who issues the permits). 

This is provided for in the Electrical Code by giving AHJs latitude to set grounding standards to suit local conditions.  You are like the 10,000th person in their jurisdiction to have that problem.  They have compared notes with other AHJs nationally with similar geology.  They know how to solve it.