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This is the place to post your ideas, thoughts, questions and comments as relates to general boatbuilding and reconstruction techniques and procedures (i.e. recoring, epoxy, fiberglass, wood, etc.)
I would do the following...
Apparently there's some 'play' between the core and the cover (that's why you have the core standing out).
Starting from one end of the jib sheet, "milk"(*) the rope all the way towards the other end. Do it a couple of times. This will "align" core and cover.
Cut both ends in the point the cover and core last meet (so you don't have extra core nor cover).
Burn the ends.
Whip the ends and lock stitch them (if you have trouble with this I'll try to find out a video or PDF that shows how to do it)
Go sailing :)
15 minutes work. Just did it last night on my new boomjack rope.
(*)If you're not familiar with the concept of "milking" a rope here's how you do it: https://www.youtube.com/watch?v=JpEDCHu9rnA
(you can do without the yellow rope apparatus and just use your hands - use gloves, it gets hot)