Repair Fly Line?

[strangercreek]

It looks like I have found myself with a similar problem. I have a WF line that is broken in the running line, right behind the taper. The core is still intact but the coating is broken all the way through, completely around the core.

I am able to put a good amount of pressure on it by pulling so it seems it would hold up under fishing conditions, but what should I do to patch it so that is will still slip through the guides? I hate to replace it already. I evidently did this when pulling on the leader/tippet when trying to unspool the reel enough to rig up the rod (if it does not come off easily next time I will know NOT to do this as 6x flourcarbon apparently slices through fly line coating )

I would hate to cut the core and loop it back together since it is still intact.