Embarrassing confessions time: The noise was due to an unlubed and original chain. When I demounted the tire, I found the broken-off tip of a cheap tire tool.
Tightened up the seat bolts. We'll try again. The rims that came with the Continental are cheap alloy rims with a freewheel that might be worn out. The paint job is gone. The kid who owned the bike before me stored it outside and covered it in cheap stickers. Lotsa rust, but plenty o' metal on those frame tubes. The Conk will live at my parent's house for my use when I visit.
I'm not a navy guy, but considering the Schwinn's weight & battleship-quick handling, it fits.