I guess I always "assumed" that the sway chains would tighten up when I lifted the 3 point to the full upward travel and never tried it. I'll have to try the crossed chain option to see how that works.You need to shorten your sway chains.
I accomplished the same thing as a retrofit by running a turnbuckle from the right lift arm back to the left pin and visa versa. This X created the triangulation needed to keep the hitch from swaying, but allowed free range of motion without buckling or binding.
.......... I've also thought of the solid drawbar kit also, but then I have that sticking out beyond the 3 point which would surely be wrecked by the logs. Sometimes I even push the drawbar under the log to pull and then that solid drawbar would definitely be in the way.