Are the shocks adjustable? Try more damping. I'm nearly certain this is the key.
Front bar will help - does way more than rear bar in terms of controlling body roll. Tires (specifically sidewall stiffness) have an incredible impact on the level of floaty-ness feeling but you will trade ride comfort in exchange for something good and stiff like the RE71r. You can change bushings to your heart's content but I don't think it will significantly improve what you are describing.
Front bar will help - does way more than rear bar in terms of controlling body roll. Tires (specifically sidewall stiffness) have an incredible impact on the level of floaty-ness feeling but you will trade ride comfort in exchange for something good and stiff like the RE71r. You can change bushings to your heart's content but I don't think it will significantly improve what you are describing.