The question is what would convince the Heritage Organization that a restoration would be a worthy project. Many would point to an elevated ranking as measurement of successful 'restoration'. A smaller group (a minority even on GCA) would say an accrurately (or reasonably accurate) restored design...however one of the reason the latter group is small is because very few are able to recognize if a restoration is "pure, clean and mostly complete". I guess it would depend on the mind set (and golf architectural expertise) of the orginization as to which arguement might convince them.
If you are looking for courses whose ranking (or prestige) benefited from a 'restoration': Salem, Sea Island, Pasatiempo, Newport, Balusrol-Lower, Olympia Fields, Yeaman's Hall, Baltimore, Valley, Camargo, Bethpage, Aronomink, Skokie, Cape Breton and even Yale. Some accurate, some not so accurate--but all considered good 'restorations' by the majority of golfers. The danger in going this route--IMO--is that you might spark a psuedo or half-assed restoration.
You could also add Cypress Point, Pebble Beach, #2, Merion, Oakmont, NGLA, Seminole, SFGC and Prarie Dunes--although their prestige wasn't effected too much and again some accurate, some not...
Others that come to mind--Fenway, Ekwanok, Beverly, Lake Sunapee, Scranton (I believe Ian A. is restoring it), Lehigh, Broadmoor, Lookout Mountain...I've heard mostly good about these, although not unanimously positive.