Is it single ply linen, or 2/3 ply? I've been fiddling about with linen strings on heavy bows recently as I've never been comfortable with them. I use 20 strands of 3 ply linen for 110lb bows, and that (when glued with hide glue) is about 2.5mm thick. If you're using normal (let's call them "modern") loops (made like FF strings with the loops laid in) just hanging out of the sidenock you will almost always have issues. With horn you're likely to get away with it, but not with self nocks. You really want self-tightening loops on sidenocks, so pass the bowstring back through a much smaller laid in loop and you're good to go. They fit snug into the sidenock, zero diagonal across the bow.
Don't ask me about unbracing them on really heavy bows, I still haven't quite figured that out yet...!