Does the sway bar pass through the k-frame like an e-body? I think it does from what I remember? If so years of jacking up the car may have bent the bottom of the k-frame causing clearance issues. If so try inserting a piece of square tubing up there and using the right size bolt and nut to spread the bent part back, or a wrecking bar if it fits to pry it back into position. If it hits the top portion of the k-frame them yes as you mentioned you can shim it down.
Hope that helps.
Brad