Dan,

Here are a couple of things to check:
Clamp a 8' 2x4 to the side of each main wheel and measure the toe out or toe
in with different fuel and cabin loads.  Too much of either could cause a
shimmy. When brake is applied the length and flexibility of the spring style
FG main gear causes toe out. My experience with a RV6 was a little toe in
solved the shimmy and tire wear.

Steve Colwell  Legacy RG