I have seen the following done with polyethylene and pvc so it might work with Nylon 6 but 3/4 inch splits may just be too large and the melting temperature of nylon 6 and polyester are getting fairly close.
(1) First you must use heavy pliers which have 1/2 or 3/4 inch tool steel machined blocks, 1 inch long, welded on the ends so that they line up exactly and in full contact with each other when the pliers are closed. The long axis of the blocks is perpendicular to the long axis of the pliers. The blocks and pliers for communication size wires are of course a lot smaller.
(2) When the pliers are closed and the blocks are firmly held, a precision hole is drilled perpendicular to the long axis of the pliers) through the blocks such that 1/2 of the hole is in each block. Thus when the pliers are opened, each block has a precision groove in it. (I hope you can visualize this.) The diameter of the hole? The diameter over the nylon 6 insulation.
(3) Then you have to design build a small temperature controlled hot box on a stand to get the end of the pliers up near the melting point of the nylon 6. (The end of the pliers is kept in the hot box when not in use.) Once the pliers are hot, it is very easy to keep them that way.
(4) Then you strip some of the nylon 6 insulation (as a tube) from one end of the wire and save this as repair material.
(5) With a safety razor blade, cut off a piece of the tubing and slit it down one side.
(6) Place the slit tubing over the damaged area (Locate the slit on the far side from the damaged area.) and wrap it with one layer of 1 or 2 mil polyester tape 1 1/2 inches wide (wider than the blocks on the pliers). Discard the piece of tape after use.
(7) Squeeze the hot pliers over the polyester tape to melt and flow the nylon into the damaged area.
(

Remove the polyester tape, trim the excess with the safety razor blade and flex the nylon insulation to make sure all is OK. Some even use very fine wet/dry sandpaper to smooth the repair.
With a bit of experimentation and practice (on an end piece), a repair worker can get really good at this and of course the color, if any, is identical as is the nylon.
The only concern then is the repair cost as opposed to the remake cost. I hope the subsequent operation was not cabling.
Perhaps others readers will have more suggestions.
Kindest regards,
Peter Stewart-Hay
Principal
Stewart-Hay Associates
www.Stewart-Hay.com