Thanks for the help, everyone. I wouldn't call my hammer technique "tapping" but the stem is now unstuck and the headset is refurbished and reinstalled.
So, I showed up at my usual Saturday morning group ride and unexpectedly came home with project bike #2. A cycling friend knew of my new hobby and pulled a 1953 Schwinn New World (K42380 is the sn) out of his garden where it was used as decoration. Yet another ladies bike, but I'm really fascinated by the head badge. It's from what used to be my favorite local bike shop, which closed in 2012 after 95 years in business. It's probably in better shape than the Western Flyer - just needs a thorough cleaning and new tires. Everything seems to be there and it's almost entirely original.
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