I have thought about getting thicker bars as well as I have always felt my car was undersprung. You mess up the balance of the Hotchkis kit in doing so though and that's why I have not changed things out.

I did get their single adjustable shocks and was getting lots of oversteer (fishtailing) at my last track day. I softened the rears and it helped out a lot.

Does the big block have alum heads/ intake or cast iron?
May be another reason why he oversteers too much. Big block torque, heavy front end, and non sticky street tires could cause that