This has gotten somewhat interesting so here is a little more. If you look at some early motorcycles they have a suspension similar to this idea with a leaf spring suspending the forks. Works fine with single tire but as you go to two tire approach as pictured the center roll line becomes important. This flat blade center spring must work in two planes, up and down and torsional. It is the torsional issue that needs to be addressed as the chassis meets a bump or pot hole. The flat center spring will try to avoid a twisting motion, this will cause the chassis to roll to configure this the rise or drop, the sway bars do nothing more than try to balance the wheel load. Adding a stiffer bar will only make the roll resistance stiffer and that looses the ride and a soft bar that is lesser than the torsional twist of the spring just locates the axle. In either case in the driver seat you end up bobbing and weaving from being to soft or to stiff. The question as to the effect of friction material for shock dampening is limited in this application. In your picture you are pinching a friction material between the sway bar arms, while might work when the axle operated evenly it doesn't when the axle twists. Friction shocks work on the surface area of the friction material in this case it is so small that it will not do much for motion canceling. The distance that the sway bar actually contracts in wrap would have to be determined so that when the chassis was in roll it did not bind severe enough to lock up. If anything this would just produce a harsher ride. Shock absorbers are a better approach. If you want to continue this approach alter your design by substituting twin torsion bars in the position of the sway bar. Both the spring and the torsion arm work on the same plane and the torsion bar rate can act as a roll control.