Have you tried just shoving the string in there? What I usually do is fit the ball end in the socket (i.e. the string pointing in the other direction, away from the nut), pull the string so it's perpendicular to the bridge, and shove the end of the string into the tailpiece with pliers or something.
If I can get a .135 D'Addario tapewound string with a silk overwrap into a tailpiece, you should be able to as well.
Rotosound nailed it - their silk wraps are rather narrow at the ball end, so I never have a problem with thick strings. Heck, my Buzzard is rocking a .140. They "taper core" their .140 string for about 5mm, so it clears the tailpiece, but the entire thickness string sits over the saddle like normal.