OK, first round of results are in. None of the test screws were successfully removed, but I think I have a method figured out that's working for me - just need to go by another tool.
Meet the test subjects:
(3) #6 sheet metal screws driven 3/8" into the playfield then cut off.
I tried Tracelifter's method first. To begin, I drilled a hole just larger than the threads immediately below the stuck screw. Drilled down until I hit the tip.
Then a couple solid wraps with a pin punch. No movement at all. Tried again and really wailed on it, but again, no movement.
I later found my concave nail set and gave that a go too, without any luck.
Next up, I tried the blownfuse/mof method. I made a little guide out of some scrap plastic.
And clamped it over the second test screw.
Since the screw is too thin to use a center punch, I started by drilling a tiny pilot notch in the top of the screw.
I reapplied the guide and swapped out the bit for one the same size as the screw body. This went well for about 5 seconds until the bit danced slightly to the side, moving the template and taking out a little chunk of playfield.
Probably my own fault for not clamping down the guide tight enough or not holding the drill steady enough, but regardless, it revealed the immediate risks to the playfield art involved in this method.
Finally, I thought about Vid's method with the hollow extractors (Woodcraft isn't open yet, so I haven't been able to buy the bits), but I realized that I already exposed the tip of the screw with Tracelifters method. I grabbed my Dremel and a diamond tip cutting tool and cleared out some wood around the tip of the screw from test 1.
Progress, finally! I was able to grab onto the tip with some needle nose pliers and twist it slightly back and forth. My problem now is that the only pair of needle nose I have that fit into this tiny hole are some light duty ones I use for board repair. Anybody know where I can find the thinnest vise-style pliers?
Thanks for reading!