I would put anti-fatigue mats (the cushiony mats you stand on) all around my LA area so you don't break the cone when you drop it. My LA is in a carpeted room so no damage done if I drop anything, including the bobbin case which can also be easily damaged from a drop on a hard surface. I have never had that happen (the plastic core break) but I don't use CT poly thread, not a big fan. I much prefer Glide or Isacord for a 40wt poly.
Edited to add, can you use the broken core thread on your domestic with a cone stand for piecing?