My pyrography tool is basically a repurposed soldering iron, and SO cheap that you’d question how safe it is.
No tool method is putting your insets knurled side up in a cast iron pan and into a hot oven. Then press your plastic part straight onto the inset, a bit trickier since you’re sort of going in blind but easy enough.
I think the blow torch method is for if you have a drill press or something similar. Put a threaded steel rod in the chuck, long enough for the heated section to be a good distance from the plastic part and the drill chuck, screw the inset onto the other end.
This seems like the most accurate method by a long way, but I have neither blow torch or drill press to actually test it.
I liked your drill press idea, did some research and found a machine that’s basically a soldering iron on some linear rails so you can press inserts in steadily and ordered one. It’s definitely gonna be better than pliers and a blowtorch lol.