i am no expert, but i have been "fidding" for the past year or so. In my Brian Toss dvd he will secure 1 end of his line with a knot to eliminate slippage of the core and then tied around a table or similar mount so he can work/pull on the bitter end of the line.

he "relaxes" the line by mushing it together (making the diameter fatter) and then uses a fid (or similar) to "reach" inside the weave of the jacket. Digs under the core and pulls out a loop. he can then simply pull out the desired amount of core.

be sure to use fresh, new scraps of line. line that has been used (even 1 time) is 1000000 times harder to splice (In my experience)

hope this helps, hope its correct