Did you try reground balancing at the waterline, black sand rolling over the coil will cause chatter like you described, does the same on excal at waters edge.
If you are getting a lot of chatter in the wet salt sand or surf. First do a GB in the wet sand area of the surf/tide line, then if it is still chattering, put GB in tracking as recommended by the manual. Simply having sand in the between the coil and cover should not result in a lot of chatter. Are you noticing black sand or other signs of mineralization? Beach 2 should be the most stable mode of all. You might also try lowering sensitivity a tad if necessary.
Did you try reground balancing at the waterline, black sand rolling over the coil will cause chatter like you described, does the same on excal at waters edge.