Just do like I suggested and destroy / remove the plastic by crushing / snapping it with a pliers and using diagonal cutters if needed to start a cut / break.
The plastic should easily come off and leave individual pins still soldered to the PCB.
It has soon became obvious that with the tools I have, it is the only option. With some CHP170 wire cutters I cut in between pins and removed the larger plastic part. I had not realized it, but the body is made of a layer similar to the one in male headers, with cutting indentations and then a larger piece on top. I had to cut in two passes. Then desolder/pull pin by pin and wick and cleanup.
Now is to be seen if the kit still works, after all the heating torture and mechanical stress.
One learning point is that I need a decent vise, so I just ordered a PANAVISE 381.