Dan,
From your description, it sounds like a racing bike. I assume you are sure it is an Herse and not something relabeled? The serial number does sound correct. Some of these racing bikes had no braze-ons, others had some. I've seen them with and without brake bosses brazed on, with and without internal brake cable routing, with and without front derailleur braze-ons, etc. Yours is more "racer" than most, in that it has Campy dropouts. Most I've seen have vertical dropouts. Probably rides great, like most of them do. Does it have the "French-style" lugs (like most Herse and almost all Singer), or the "Italian-style" ones?
A lot of people in the U.S. who bought Herse and Singer in the 1960s and 1970s didn't want/understand randonneur bikes, so they ordered racing bikes. "Make me one like a Cinelli Supercorsa" is what they must have said more or less. Almost all Singers that were imported by Spence Wolf at Cupertino came as frame and fork only and followed that spec. Herse and Singer were happy to oblige, a racing bike being so much easier to build than a randonneur. (I even have a Singer with braze-ons for those awful Blackburn "Custom" lowrider racks! Why Rodriguez, who ordered it, didn't go with a Singer rack must have been a matter of money.)
The lack of clearance on your bike is surprising on a 1961 racing bike... Do you have photos?
Good luck,
Jan Heine, Seattle