Don't forget that you'll also need a new headset and stem. LHTs will also generally have a shorter top tube because they expect you to put your hands on the hoods. At least usually.
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Bikes: 1996 Eddy Merckx Titanium EX, 1989/90 Colnago Super(issimo?) Piu(?), 1990 Concorde Aquila(hit by car while riding), others in build queue "when I get the time"