While reading up on playfield restorations to educate myself I came across several questions on removing blind nuts from the playfield. Here is a quick safe way that comes from my Model airplane hobby.
I am in the middle of a cleaning/restoration of a STTNG and I wanted to clean and sand the back of the playfield and then seal it before tackling the top clear coat. Most of the blind nuts are installed in a routed depression but some are just banged into the back of the playfield. I want to remove those to make sanding easier.
They are not glued in which makes them easy to remove. You could just thread a screw into them from the back and probably pull them out, or you could use the screw from the front and tap them out from the front, although I prefer to keep hammers away from the painted finish
This method pulls them up straight and easily from the back. You need a small piece of PVC pipe or similar that sits around the blind nut. I used a small piece of 3/4". You need something stiff to span the top of the piece of pipe with a hole in the center for your screw. I used a piece of 1/4" aircraft ply. A proper sized cap head screw and washer is used to pull the blind nut straight out.
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I had 2 sizes of blind nuts on the back of my STTG. The 3/4" PVC fit around both of them.
Hope this helps someone