Old Jiffy Ice Auger Model 30 pull cord help - Can't remove old cord?

I have a 19-year old Jiffy Model 30 auger (bought Dec. 1999) with a Tecumseh AV520 engine.  The sheathing on the pull cord frayed the other day (cord didn't snap) but it caused the cord to not be able to retract all the way.  I watched a couple YouTube videos and the fix seemed pretty straightforward.

I bought a new cord from a local lawnmower/chainsaw shop, pulled the cowling off, pulled the cord all the way out and locked it in place with a screw driver.  All the YouTube videos show all I need to do is snip the cord on one side, and pull the knotted end out from the inside, then re-thread the new one, tie a new knot, remove the screw driver, and let it rewind itself.

Problem is, there doesn't seem to be a knot at the end of my cord.  It comes through a section of thicker black plastic and just pokes out the other side.  I've tried tugging on it with needle nose pliers and even some pointy wire cutters for better grip, but it won't budge.  Something other than a knot seems to be holding it in place.

Any small engine guys here have any ideas?  See the photos below.

Thanks!

I hope there's a simple solution I'm just not seeing.  There looks to be pins just pushed through the plastic. I tried grabbing them with fine wire cutters to try and pull out, but they just broke off.  Bad design, clearly.  I can't believe that Tecumseh designed a pull cord that's permanently attached to the engine recoil, so I have to replace the whole recoil for $30 instead of being able to put a $2 rope on it.  Hope not!