Update time:

I think the seatpost problem is getting solved, thanks to Pastor Bob's generosity.

Headset is still an issue. I have it all apart, and all the bearing surfaces look amazingly good. Problems: the crown race spins on the fork (but the key lock works!!!), and the lower fixed cup does not want to come out. On a trial reassembly the fork still binds when I turn it 90 degrees from straight, and the bind point moves around. The fixed cup seems very flimsy compared to those on high-end bikes, and I think it's rusted in place near the alighnment key, while loose elsewhere. There is a gap between the bearing cup and the frame edge at the back of the headtube, that is not present at eth front (rusted) edge.

Due the welded-in alignment key I can't use a standard "rocket" tool to force the cup out, and I think I'll need a replacement anyway. For the crown race I think I'll see if the LBS is up on the knurling technique.

Anybody tried to get a Schwinn replacement for these parts?

The BB seems rough, too, but Harris has a Tange replacement available.

Road Fan