This doesn't apply to spedsters, but there are several companies (Art Morison for one, http://artmorrison.com/homepage.html, who will take your old GM car and adapt a modern driveline and engine so your replica handles just like a modern car while remaining completely stock on the outside.
My favorite is a 60 or 62 Corvette with either the original frame, or a custom frame, modified to accept a complete C4 engine, driveline and suspension. That would be my particular aspiration (when some money falls from the sky).
Fortunately, IM offers us a similar choice using Porsche components. SAS, with there Subaru front and rear suspension, might be a contender if you are patient. Probably some like these are found in Europe too.