I'd try running the engine up to temperature first, and giving it a good rev. Screwing the threaded bit back in and going for a drive isn't a bad idea, but a bit decent rag wedged over the hole would be enough to catch the projectile.
Failing that, drilling is the next step. You'll usually find once you get down near the end of the thick section, it'll start spinning. If you're lucky it'll catch on the drill and just pull out, but starting the engine up will blast it out, along with any crap/swarf.
Failing that, drilling is the next step. You'll usually find once you get down near the end of the thick section, it'll start spinning. If you're lucky it'll catch on the drill and just pull out, but starting the engine up will blast it out, along with any crap/swarf.