You didn't say it had a carbon fork. If it had the original steel fork then threaded/quill stem would suit it better imo. But since it has been altered (why?) with a modern carbon fork and perhaps other modern parts, theadless won't matter as much aesthetically or period correctness-ly. But finding a suitably sized quill stem will be your cheapest route, perhaps you can trade? Nitto pearl stems are nice, not Ti but high quality alloy.
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1989 Schwinn Paramount OS
1980 Mclean/Silk Hope Sport Touring
1983 Bianchi pista
1976 Fuji Feather track
1979 raleigh track
"I've consulted my sources and I'm pretty sure your derailleur does not exist"