The farther back you go, the more relaxed you're going to get, and still maybe get Italian, if that's what you have your heart set on. Someone mentioned Legnano earlier (although I've never seen one bigger than 58cm; and I've looked).
And I know they don't come up often, but my Grandis (probably a 1971) is pretty relaxed. Mine cost exactly $500, as it happens.
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● 1971 Grandis SL ● 1972 Lambert Grand Prix frankenbike ● 1972 Raleigh Super Course fixie ● 1973 Nishiki Semi-Pro ● 1979 Motobecane Grand Jubile ●1980 Apollo "Legnano" ● 1984 Peugeot Vagabond ● 1985 Shogun Prairie Breaker ● 1986 Merckx Super Corsa ● 1987 Schwinn Tempo ● 1988 Schwinn Voyageur ● 1989 Bottechia Team ADR replica ● 1990 Cannondale ST600 ● 1993 Technium RT600 ● 1996 Kona Lava Dome ●