You could go further and using your original jig, pack it full and cut to length at the band/table saw. Install a air hose coupler at the dowel and a shot of compressed air would liberate the strands. Being substantially longer they should be easier to police up around your shop that the short auto-cutoffs that put you down on your knees.
Thinking further, maybe a washer that fits into the tube, long screw through the washer to create a plunger. Shaft of the plunger through a hole in the dowel. When done cutting, push the plunger to expose an 24.5mm or so length to grab onto and pull the buggers out.
The thought crossed my mind till I saw the clips... I don't mind being creative but sometimes too much thought can eat (is that the right word?) into valuable drinking time.
Bazza's intro reminds me of a duck in a my spa.
If your first cut is too short... Take the second cut from the longer end... LBD
